I actually managed to fix this, but you won’t like the way I did it…
The problem seems to be in the flight_model.cfg file of the aircraft, which is in the Microsoft Flight Simulator Packages\Official\Steam folder for me (in each aircrafts folder).
These files might not have been updated with the latest patch, for different reasons, which would cause the uncontrollable aircraft upon landing and also the A/T issues.
What I did was, I deleted the files named flight_model.cfg, then did a “Check File Integrity” for the game and it redownloaded these files. The problem is, it also redownloaded a lot of other files for the sim, so you might want to try an alternative fix unless you want the game to redownload most of its files again, which will definitely fix it if you have the time to wait for 100 GB+ download.