Why is my carved hummingbird cracking where it meets the branch?

That crack at the base is almost certainly wood movement, not glue failure. A thick oak offcut is basially never fully dried, and oak in particlar keeps releasing moisture for ages. Meanwhile your twig is thin, so it responds to humidity changes way faster than the base does. Two woods shrinking at different rates, joined rigidly with a tenon, means something has to give, and the glue line is where it gives. The crack near the feet is prolly the twig itself checking, which points to the branch not being fully seasoned before you carved it.

I killed a little carved wren the same way years ago, sat it on a chunk of dried board and watched the twig split at the feet. What actually changed things for me was a cheap moisture meter, the kind you stab into the wood. Turns out my 'seasoned for months' sticks were still way too wet inside while feeling bone dry. Now I test both the twig and the base and just wait untill they read close to each other before gluing anything togather. Also started sealing the end grain on twigs with plain wax while they dry slow in the house, not the shed. Sheds swing too much with the weather.

This is making me rethink the pile of branches I've got leaning in my garage right now. I've been letting them sit there thinking time alone fixes them, but sounds like a thick piece and a skinny twig dry at totally different speeds even side by side. Does the bark being left on slow things down, or shold I strip it off so the wood dries evenly? Also wondering if keeping the finished bird away from windows and heaters woud stop the cracks from growing, or if once it starts splitting it just keeps going.