You could try jamming a small teaspoon on the edge still inside the stick socket and rim around the base of the stick until it pops back in.

The plastic will most likely deform on the dome at the base of the stick and scrape, still it will work until you buy replacement sticks.

It’s an easy swap, careful to not strip the back shell screws, to not mangle the shell using a bitter knife to pry it open, and to not overtighten the stick module screws.

Just take the back off, unscrew the joystick daughter board and fix it. Unless the plastic has been stressed enough so that it loses the memory and is permanently warped, it should be fine.

My advice is not to do that