Battery problems

Hello Phaetonists, I would like to ask you for your expert advice. My V8, BJ. 2003, 270tkm (i.e. just entered) has problems with the power supply. If the car stands more than 2 hours it does not recognize the key, the central locking does not work, the clock is adjusted and various other electrical problems occur. I drive the car and make a short stop everything works normal, after a longer stop (more than 2h) again not. Clear case, the comfort battery I thought it was defective. I was amazed to find out that the comfort battery was from 2012. Installed by a VW dealer from Neunkirchen-See. That was the last thing the old owner did before he sold the car. Questions: Is it right that the alternator would have to have a healthy battery after a long drive (about an hour without an extreme power consumption) so that the battery has enough voltage until the next morning? Does it make sense to use the battery? Is the right battery installed? Pb/ Ca VW standard 750736+TL 82506? Can you recommend a better one? How do I build the safety box to lift the comfort battery out? Need a few more photos of the comfort battery (in the direction left under the fuses) – starter battery (in the direction right behind the grid) – the sticker from the comfort battery – the accompanying booklet from the comfort battery Thank you for your answer en kidston