Every car generation has it's kinks: older TDI Passats and their BSM.
Problem with the newer generations is the cost of repair, but back when the older were new, a 01M replacement or 5spd conversion was much more expensive than nowadays.
Pointer: do not drain the coolant, as other people report issues with purging the system (I didn't). I just removed the water pump and replaced the coolant that drained that way. Just top the bottle before you start the engine, mine took almost a gallon back in.
Also, there are replacement...
Ask the dealer for their offer, that would be an easy data point. Also online services like Carvana could be easy data points.
Car prices are locale dependent, so you need data points around you. No idea of prices as of late, but I had to travel to find both my 2015, most likely because I wanted...
Also, if not with the original radio, the dead battery could be the result of the canbus never going to sleep with an aftermarket radio. Heck, even OEM newer radios (if retrofitted) require update to the canbus, one from a newer model jetta.
You will be fine for 18 months with a new battery, best not to cheap out and get a dealer sold battery if you have a dealer nearby.
That jetta (engine code BRM) most likely needs a new camshaft and lifters. If you listen to the engine running and it taps kinda hard, it probably has a hole in a...
For mk4 and trying to stay as close as OEM as possible, I did RCN210 for a little over $100. But my car has a quad connector and steering wheel controls, so I had to spend some other $40 or so for the Canbus emulator/quad connector.