We had frogs as both villagers and catchable "fish"(not to mention tadpoles).
Same goes for octopi.
We also had Tortimor(and maybe Kapp'n and his family) andcatchable soft-shelled turtles.

So why not have birds as villagers and catchable animals at the same time like the above?

hmm mister h. that sounds cool in my opinion.

It might already be obivious but most likely well be birds you find in Japan since I know for sure all the fish and insects you find in the game are all in Japan. To me I still find it crazy to think about that lol.