New extractor fan fitted!
We found out why the previous fan was glued in; because the previous owner had bought a fan too small for the hole that he'd made in the plasterboard (there's a wooden frame inside for the fan to screw into) and decided to just glue the one he'd bought in place.
Thankfully the one I bought was big enough to screw into the frame and is working much better at extracting. :)
@renbymon That is so absurdly jank...Glad your new one fits better! It looks good, I had no idea Bosch made extractor fans.
@renbymon SUCKY SUCKY!!!!!