Nintendo originally stated that the Switch was a "home console first", but then they released the Switch Lite, which is a "dedicated handheld". So it really belongs to both categories, as it can be used as either a fully functioning home console that never leaves the dock, or a fully functioning handheld that never touches the dock.
Based on some other communities I've seen, the Switch should be classified as a home console when you're negatively comparing it to the other home consoles and a handheld when you want to praise devs for 'getting something like THIS running on a handheld' :P
Nah but serious, I'd just classify it as both, cause that's what it is, ya know? (Switch Lite excluded, obviously, that's just a handheld)
It's primarily a handheld which is now even more obvious thanks to one of the models being exclusively handheld. I mean, nobody would argue that a phone is a home console but you could set it up to a TV it you really wanted to.