TBM 930 AP randomly decides to only honor all altitude modes, but not direction

Lately, I have been facing a certain peculiar issue with the TBM 930’s AP.
Each time I take off and engage AP, a dice roll happens to determine IF:

  • AP functions exactly as intended and all modes work flawlessly
  • AP altitude related modes function as expected (ALT, VS, FLC all work fine), but HDG and NAV only function visually (changes in Flight Director overlay and visual yoke position). The plane simply continues flying in whatever direction it was flying, completely ignoring the AP-steered yokes. I can even steer the plane manually without any corrections coming from the AP in HDG or NAV (regardless of CDI setting). There isn’t even the extreme banking issue which typically manifests when actively taking over without disengaging AP first.

This does happen on a clean (deluxe/premium only, no marketplace or community addons) setup as well as with mods that directly involve avionics (e.g. WT G3000). Happens without a flight plan, with a plan set in main menu or with a plan set in avionics. Happens at any kind of takeoff - starting cold & dark or on a runway.

There are no controllers connected to the computer and none shown in joy.cpl or Device Manager. The control presets are default keyboard and mouse ones. And once again, I can manually steer the plane without any problem once the issue manifests, so it is not a stuck key - a keyboard only knows fully pressed vs not pressed, unlike a controller.