How to troubleshoot:
Get a needle and make a small hole in the bulge on the back.
You will get either nothing (the bulge will stay the same), or refrigerant (the refrigerant itself has no or almost no smell, you may or may not not sense the smell of the compressor oil, but the bulge will soften), or water.
Be assured that puncturing a single small hole will not make things worse.
Nothing = the problem is elsewhere. It may even be this way from the factory (some extra foam injected in this place).
Refrigerant gas = refrigerant leak.
Water = condensed water leaked in a pocket.
Contrary to the other answers, a lot of modern fridges do have a lot of gear hidden in the back. The usual suspect for a single-compressor fridge + freezer is a heat exchanger for the lower part. If there is a refrigerant leak, this is unfixable at a cost comparable to a new fridge. As far as I remember, this particular model was available at least in 2021 and maybe even right now.
It was not stunningly expensive either.
Water = some low-pressure tubing for condensed water gone bad. Fixable with moderate skills and some swearing. On the other hand, this does not explain the bad cooling. It may be the thermostat (only the lower part temperature is regulated). Or, the thermostat may be ok and just set too high.
Good luck fixing it. My wife wanted the same model but we considered it way too small for our needs.
Edit: since the refrigerant leak is confirmed, this is (roughly) how it could be fixed:
- Disassemble it from the back.
This requires removing the glued cover and the injected foam (be ready for an incredible mess).
If you find the approximate location of the leak in the process, good.
(failing to spot the leak) find the leak using soapy water, refrigerant detector, by ears or otherwise.
Get a replacement of the leaky detail. Good if it is a tube, good if it is some copper alloy.
Cut the tubing at the appropriate places, replace the leaky detail, weld / solder it in place, attach it wherever it belongs.
Vacuum the system, check for leaks, refill with the proper refrigerant (and compressor oil), check for leaks again, check for proper operation while everything is open.
Get polyurethane foam and fill the voids back approximately to the previous state.
While the foam is still not set, put the back cover in place.
Caveat 1: in most of the developed world, one needs to be certified in order to deal with refrigerants.
Caveat 2: refrigerants for small cooling devices (e.g. fridges) are different from the ones used in A/C units. It may prove hard to obtain the refrigerant or hire a competent technician, because small devices are quite rarely refilled. People tend to disassemble/refill or even build fridges only in rather expensive contexts - e.g. fridges for yachts or motorhomes.