Unfortunately, Android made major changes with regard to NFC's "is the screen on and unlocked?" functionality.
It has something more going on than in the usual place where the "trick it into thinking the screen is on and unlocked" modification is made.

I've tried a few approaches and failed.

This likely requires someone with much more talent and skill than me to dig into the new things.
Once that's figured out, maybe I can do the maintenance side of keeping it updated with minor changes Android introduces.

This module may be at an end with Android 14.
Even then, it may eventually fail to work on non-Google devices receiving regular Android 14 updates since I can't do easy testing without one of those devices.