Problems with battery voltage followed by gear problems although new batteries

Hello Together, as a long-term (silent) reader I now have a serious problem with my diva, whereupon I post my first post here and hope for tips and/or advice, thank you very much in advance. Key data: 3.0 TDI, 239PS, BJ. 2010, mileage 210K 0603/AUT000048 With o.g. mileage never had problems, except of course wear parts. Both batteries (board net and starter) were still the original ones (2010). Until last year at the beginning of the winter time November 2022 I had the Reported when ignition “Please start the engine”, which I initially ignored until at some point aut. tailgate, window lifter, MFA no longer worked. Of course then driven to the friendly on 11.2022 and renewed the power supply battery (VARTA G14 95 Ah). Then no problems….until next winter. Now now 10.2023 again at autumn/winter time the same message when ignition in the MFA “Please start the engine”. Well now again driven to the friendly and this time the start it renews the battery (Varta 60Ah). Nevertheless, I get the message again and again (batteries both new) with ignition “Please start the engine”. This went then as far as yesterday morning the following pass is: Key in/Zündung an –> Everything dark (MFA/Tachometer) started 3 times loud beeping engine –> in gear position R switched –> there was a violent jerk first. Then in gear position D turned –> again violent jerk. But I started. In the MFA no gear indicator visible. and the rides I noticed that the Diva does not switch higher than the 3rd gear, i.e. I drove 5 km of highway only max. 50 km/h (emergency run?). At the finish arrived engine off –> 30 min. Later ignition/engine on and normally returned home as if there had never been anything 🙂 Now to my 2 questions: 1. Voltage on the on-board grid not sufficient despite 2 new batteries? Still consumer? LiMA? 2. Can the defective voltage affect the transmission? r with you to get help and if necessary tips on how I could/should proceed here. Maybe the one or other similar problems with battery voltage/gear and happy and thank me very much for any answer. Greeting Alexs_87