Just had the same problem with a bottle of wine that must have been slightly taller than usual. It got wedged in and then I couldn’t open the bottle opener.
I tried brute force but ended up pulling out the handle and damaging it at little, so definitely don’t just yank on the handle as the pins are plastics and quite delicate. Instead, try pulling the top and sides out of the unit, gradually increasing the gap until you get to the middle and can get your fingers in both sides. And then pull hard outwards. The unit should pop out exposing the fuse box. Take a look at the manual and you’ll get a feel for the size and shape of the bit that your pulling out and how to refit it.
It still took a bit of time to extract the wine bottle, but there was much more leverage with the unit removed. And then the whole unit just slotted back in (again see the manual for replacing the unit over the fuse box).
Anyway, I also learned something new. There’s a purpose built knob at the back of the wine holder that will divert air conditioned air into the wine to chill it. Or you can close it if you want can temperature. You can access this just by looking inside the wine holder and at the back!