I think that giving Mario Odyssey lots of good vibes of Super Mario Galaxy is a great thing to try out, although I wonder if it removes one of the key aspects of Odyssey which is that it's not Galaxy. Some galaxies like Freezeflame, Dusty Dune and Melty Molten Galaxy were already, how to say it, they were using an entire planet and rarely anything besides that, which most galaxies didn't have. They can easily take this further, although in my opinion, I would prefer to see this happen in a Galaxy 3 game and not Odyssey 2.
About characters returning, yes, so much yes, that would be neat! A minigame like the Koopa Freerunning game, but you have to beat Nabbits? Things like that. For what concerns kingdoms themed around different Mario games, well, that's where I'm getting a lot of inspiration from for kingdoms. There are plenty of Mario Party boards and 2D worlds that would be so nice as a Mario Odyssey kingdom! I'll talk about them later because I got loads of 'em.
Edit: To build on this idea, I've always had the idea of, instead of launching a new controller with yet another New Super Mario Bros. game which barely shows the system's capabilities at this point, to make a Mario Generations game: an open-world exploring game where many of the old games' worlds are recycled to create something new. Like Throwback Galaxy from SMG2, but much more of an overhaul. Some examples are Dinosaur Land, which was a world in Super Mario World. Imagine all of the beeg beeg Yoshis wandering around in a prehistoric jungle world? Or a Cool Cool Mountain which is much larger and doesn't have cliffs surrounding the top? The mountain is actually located right in the middle of a giant snow world! How about Mario Party boards like Yoshi's Tropical Island? Well, that island is reality in Mario Generations! This would be so good when they make all these 'kingdoms' bigger than the kingdoms in Odyssey 1 are. Can't wait for Nintendo to realize that New Super Mario Bros. is no longer new and Mario Kart 9 is very limited compared to a game like this.
While I also think it's a good thing to try out, there's also a risk of not, well, taking risks. That is, a new game that takes too much from Galaxy can come off as not being confident enough with its own ideas and can fail to stand out as a new establishment. It's why Galaxy 2 in particular earned my ire and it made me not want another Galaxy game, especially not Galaxy 3. I was happy when they announced Odyssey as a new game and not Galaxy 3. I think they're pretty much past the Mario in outer space concept though. Even Rosalina's reduced to a spinoff character nowadays while the Mario series has taken another direction.
As for open world, I think that aspect of gaming was just a huge fad. It's difficult to pull off and open-world has never been a component of a Mario game before. I don't know if it can be fine-tuned to Mario's style (which is about simplicity, being straight-forward) especially without becoming repetitive (open world tends to have some extra gameplay mechanics that can complicate the games). I don't know how Mario can pull off open-world but I think Mario's better off with exploring a big-ish map with clear goals, with platforming gauntlets serving as a break from exploring. I think there's a lot of potential in using older setpieces to create a new environment, but you want to balance that with new ideas, or else you have Galaxy 2. Expanding worlds do sound nice though, like Cool Cool Mountain has less snow at lower elevations and then the higher you go, then you see all the familiar set pieces and it culminates into going inside the chimney or something.
Since it's on my mind now, I want to share my thoughts and ideas on new concepts, controls and other things like that
Starting off with new controls:
First idea is the kung-fu kick, or some sort of kicking move. Not the breakdance move from Super Mario shitstyfour, but something that's actually helpful in some circumstances. How this would work is when using the kung-fu kick, you can attack an enemy as Mario if it's close enough to you. The reason is that right now, Mario can effectively only defeat most enemies by jumping on them, but some enemies like Spinies can not be defeated by simply jumping on them. For those enemies, this will be useful. When standing close enough to an enemy, you can perform a kung-fu kick to kill that enemy. The enemy has to be relatively small - so this won't work on Thwomps or such things - and you also have to be really close to an enemy to successfully execute this new move, making it a risky move. I think it will have just the right amount of risk attached to it for it to work great.
Another new move for Mario is the frontflip, or high jump. By doing a frontflip, Mario can jump a bit higher than normal, plus, he will move with his face towards a ledge or something instead of moving towards it with his back. This enables him to hang on ledges that he wouldn't be able to catch on with a normal jump or a backflip, because then he can't use his hands like claws. I think this would be a neat new move that I think would work really well.
Obviously, a new Cappy move would also be great. I call it the Trapeze move. Remember the trapezes from Super Mario 3D World? It kind of works like that. You throw Cappy diagonally upwards, so forwards but also upwards, and then you hang onto Cappy and use him as a bridge to get further. There wouldn't be any good purposes to use this in comparison to other moves in the current moveset, but to be honest, I couldn't think of any other new Cappy moves since they are already so well implemented in Super Mario Odyssey, and I prefer finetuning the current moveset from the old game.
This might add some unneeded complexity to a game, especially with the caveats. Combat in Mario tends to be very shallow, but if you need to expand the options, you have to probably design your game around it. While Mario in Super Mario 64 does have combat options, most enemies are easily dispatched with a slide attack, and it's a lot safer than standing there and trying to punch and risk getting bodied. If you want to make punching more useful, you have to design the level kinda like Lethal Lava Land where sliding can risk you falling off but the design of the level can be compromised.
Not sure if the frontflip is a necessary move but it can replace the unwieldy backward somersault. Maybe Mario can crib that move from the Donkey Kong Game Boy game or Mario vs Donkey Kong where Mario can handstand on his own and then perform a big jump. And it can be more useful than a triple jump since a tripe jump requires space to execute.
I'm not sure Cappy requires any new moves but they need to find a way to integrate existing moves without requiring motion controls, maybe map to other buttons for starters? I mean there might be interesting puzzles designed around throwing Cappy directly up or throwing Cappy like a bowling ball. As it stands right now, they're pretty useless moves and the motion controls just make it more cumbersome to perform. The one you proposed just seems like a minor move that I can't see having too much use. You already stated the toolset is pretty good, so...
To answer some of the questions here which I feel like not discussing too much (that is everything but Kingdoms. I love predicting the places they might visit in a future game):
I could come up with three different plots for the new game. The first of which is Bowser tries to marry Peach again. What would make this difficult is they'd have to come up with a bunch of different new wedding items, different to the first game. I feel like it was already hard enough to come up with enough of those for the first game, so that makes it less likely he'll attempt to marry Peach again. Also because he failed badly in Super Mario Odyssey.
The second is that Bowser kidnaps Peach, and then takes her on a 'honeymoon' kinda trip around all the Kingdoms, and Mario is on the chase with them. All of the kingdoms will have many marks of Bowser and Peach having been there, for example, Bowser's footsteps will be visible in the sandy and snowy kingdoms, and Peach could try to give subtle hints to Mario about where to go next. Some sort of secret messages. They could, for example, go on a cruise to a tropical island, and then Mario will also arrive on that Island Kingdom. Or they could go camel riding in a Desert Kingdom, and Mario will have to do the same. Of course, there will be boss battles with Bowser just as with other bosses (maybe Bowser could prepare some bosses when he's in Kingdoms?) so they might have to come up with some sort of 'you are this close to Bowser' and when you're in the same Kingdom, there's a boss fight.
The third option I'd like to talk about with you in this post is a potential of Bowser getting characteristics of Baldy McNosehair in the sense that he will try to create a machine that will 'steal' Princess Peach's heart, so that she will forever fall in love with him. Kind of like the Binding Band in the first series, but now it's a machine. Bowser will try to gather all the special pieces he needs to build the machine with, similarly to how he collected all the wedding objects in the first game, but again, now it's a machine. And Mario will have to chase him in a similar way to Super Mario Odyssey. I think this would be more likely compared to the second option, and perhaps also more likely than going to marry again, even though I'd personally love to see a honeymoon plot in Super Mario Odyssey 2.
You guys have any ideas about plots?
Maybe they can attempt another wedding but I like to see another take of Bowser trying to partner with Peach. Actually, I think the plot should be more on Mario and Peach with their Bonneters trying to stop Bowser and maybe Madame Broodal can play more of a role. This time, they're just pillaging kingdoms like in the first game. Maybe this time they'll try to rig elections to elect Broodals and Mario and Peach have to stop them. Heck it'll be like the first one but without the marriage silliness.
I think a lot of your proposals are already in the first game. There are marks in the first game with signs of damage in the first game, and Bowser's footprints and Bowser posters (which would be campaign posters now in my idea because it was an ongoing joke by me and my sister that the Bowser posters were Trump posters) are everywhere. The subtle hints would be a neat way to guide players though given the sandbox nature, it'll have to be put in a pretty linear level since you'll be walking around everywhere to clean up the mess and get as many power moons as possible anyway. The maps have to be big or otherwise a bit tricky to navigate for that to be effective, as the base game already has a map and many useful landmarks. Tropical Island has been already done as a kingdom, and we had two ocean kingdoms, so they should really either spice up or just have another exotic location.
I'm not too big on the whole marriage thing overall. If you don't mind me dropping some more ideas, I think Mario and Peach should work together this time AND it's a better way for the two to develop as a pair. Luigi also imo should get involved because, well, he's Mario's brother.