Fascinating take! I like & agree with this notion of adopted-gender. Although it bring my mind to an inquiry on the semantics of grammar here; like you said, Yoshi's as a species don't have gender, but Main Yoshi decided to go by he/him pronouns, as opposed to "they" or "it". With this in mind, we can assume Yoshi is neither trans nor cis!Hm?
What I mean is that there would be no subconscious assigning of gender identity for a species without any biological impetus for that (ie separate sexes), meaning Yoshis wouldn't have separate genders because they wouldn't have....I don't wanna say the "capacity" for it, but something along those lines. Although it could very well be that Birdo only "thinks he's a girl" because Birdo's species also lacks separate sexes, meaning that they can't really be "boys" or "girls" by simple definition of that they are a single-sex species, and as such lack that sort of differentiation on the bottom line. Which would be less "transgender" and more "conscious adoption of a biologically-inapplicable gender."