This isn't enough to go on:
Monitor coolant level in the radiator (not the overflow) and see how much you're using over many months and checks, not just once or twice.
This is not a good way to determine coolant loss through either a leak or HG. Personally, I don't want to wait for a long period of time to see if a HG is leaking because that just means more damage to a head or the block through constant compression bypass and detonation.
Well done on the purchase. The VDC is a bad ass and the engine is hard to kill if you pay attention to it. If it comes to needing major engine work to correct it, replacement H6s are available for under $1000 and can be swapped in a day.
First off, I'd go get the car from the shop that condemned the computer and told you it needed a reflash upon installation. He's wrong. Up to 04 it's plug and play, no VIN writing necessary and the computers rarely, very rarely, fail on this generation. Someone may brick one in attempting reflash/reprogramming or water intrusion would kill it, but otherwise, no. You can pull up the carpet on the front passenger side, remove the cover (10 mm bolts) and look for signs of water or corrosion on the plugs.
If it isn't overheating and your not experiencing sporadic interior heat loss, I'd get the battery and cable condition corrected. Corroded cables and a weak battery will cause all kinds of problems.
Next would be to pull a plug on the bank 2 side and check it's condition. The deposits on the plug is an indication as to what is going on.
Then you look close at the injector harness for chaffing, cracks, wear, teeth marks. Check for injector rail or injector seal leaks. These injectors also have seals for vacuum at the top and bottom and if they are dried out, installed wrong from previous work, or whatever, it inhibits injector abilities to spray proper.
Check the coil harness for the same.
These H6s will run with a vacuum leak since it's MAP operated and not MAF. You can still check for leaks as consistent and equal air flow improves performance.
If none of the above results in a repair that works, then you go to the knock sensor, AF sensor function and compression testing along with a thorough check for a head gasket leak. In checking the HG, use a funnel like a quick fill funnel and have the car running where you can observe if air bubbles are present in the funnel, especially after the thermostat opens. You can also determine HG issue from AF data if the AF sensor is working proper. The side with the water leak will be adding fuel to compensate for the higher oxygen content in the combustion from the water.
Data logging is always a good idea and may help you later in the life of the car as things come up. If you have a laptop, look in to Rom Raider and a VAG-COM KKL cable. The software is easy to use and learn from.