Please Help A3 8L transmission skipping 3rd and clunking (FYL 09A JATCO JF506E)

Hi Folks - please help. My A3 8L 1.8T 2003 transmission (FYL 09A JATCO JF506E 5-spd auto) is suddenly skipping 3rd gear and changing very clunky up and down. Slightly better when it warms up.

Is the transmission in fail-safe/limp mode?

OBD codes say:
Transmission Electronics:
- 00526 Brake Light Switch Short Circuit To B+
- 65536 Control Module Faulty
- 00652 Gear Monitoring Implausible Signal

The car is in absolutely pristine, original body & mechanical condition with full Audi dealer maintenance history and 170,000km, and zero leaks.

I suspect low and/or deteriorated (original) ATF, and/or perhaps a sticky solenoid since there are no dead solenoid or sender faults in the OBD log. I highly doubt there's anything mechanical wrong inside the transmission since there is no slippage.

To diagnose, I am next considering cleaning all the grounds and testing resistance of all the transmission solenoids. If no faults, then changing 7L transmission fluid with VW ATF G052990A2 next.

The brake light code could be a red herring and code 65536 seems to be a catch-all for anything where there isn't a specific code, right?

Advice would be greatly appreciated please folks!
Thanks