Just yesterday I was looking up ways the reincarnate spell has worked throughout the editions, since I'd like to make my own tables for it if it ever comes up. In some editions the options included regular animals right alongside humanoids and some more monstrous options.
I think you could take some animal statblocks, use the awaken spell for guidance, and whip up a character race that is balanced against others while still having all the features from the MM and close hp. Of course, that only works well for certain animals and there are a lot more it doesn't work for.
I'd allow an awakened animal to learn to cast spells. It might be hard to do when you are just shapechanged, but when you were born in that body and have been granted speech, no reason you couldn't figure out how to make functional somatic components and manipulate materials just like dragons and other non-humanoid casters.
In the Feywild awakened plants and animals are common (and although I didnt see it written anywhere, I assume they arise spontaneously there, rather than that there are a bunch druids running around on casting sprees).
