Hi,
writing this out since nobody replied to my previous posts with any information that would help me and will also possibly clarify some things to others.
I went to get my car battery replaced by a mechanic that was recommended to me, supposedly he had equipment necessary to code a new battery for a Škoda Octavia Mk IV. When I met him I told him my concerns and he guaranteed me that he is able to do it.
He simply disconnected the old battery and reconnected the new one, without any power supply keeping the car modules powered. He also needed to take out part of the air filter intake assembly for putting in a new battery, then he "coded" the new battery on some red tablet with a proper looking OBD cable. The tablet put out some beeps that would indicate that the coding was not a success but I didn't say anything since I didn't want to be a smart ass. When the car was turned on there were of course 20 warnings but after driving for like 50 meters they all disappeared.
When I came home I connected my VCDS only to find out that nothing was coded. I did not want to go back to that mechanic since he obviously didn't know what he is doing. I tried buying a SFD token service (one more shady looking than VAG logins) but it did not work, got scamed for 10€ but whatever.
My friend came over later today and he has a CARISTA evo module with a subscription. At first we couldn't change the battery coding, but when he read and deleted all the diagnostic error codes, he was able to change it, and I was able to verify it with my VCDS clone from aliexpress. I am pretty sure a OBD11 would also work for this - random tip, on the OBD11 website, register, put OBD11 with the VAG subscription in the cart, and don't buy it. Wait for an email from them and they will give you a 10% discount.
I am now very happy and satisfied. It is very noticable that the engine starts up quicker (like 1/2 second sooner), and with the VCDS I also looked at the analysis of starting behavior, and the starter draws a much higher current, while also creating a smaller voltage drop on the battery. The internal resistance as shown by VCDS is also much lower. Will keep you updated how long the AGM battery will last me.
Cost-wise, the 72 Ah AGM battery was 160€ while I could get an EFB battery of similar capacity for 100€. Dealer's garage would charge me around 300€ without them being able to tell me if they will put a cheapo EFB or an AGM battery.