What is the light fitting and how to fix.

twopenny

"I wonder if the existing one is even broken?"
I think the large chunk of plastic that fell out= the bit missing from the fitting would answer the question 😉

WIAWSNB

If you were physically up for the task, it would be very doable. But if not, then it's a simple task for a handy person.
Do consider the suggestions made for a more flush LED fitting instead - fit and forget.

FFHillbilly

It all depends on how many wires there are when you unscrew the ring, if its wired in "three plate" and there are multiple cables it can be daunting for DIYers and I wouldn't blame you for getting an electrician in, but theres an equal chance that it's just one cable with L, N and E in which case it's very simple.
something like this for example comes with a pair of inline wago connectors and just just snap them onto the existing wires, light bracket fastens with 2 screws and the light fastens onto the bracket with a 1/4 turn twist it's about as simple as it gets