Well, it sounds as if you have covered everything I would have suggested and a couple I wouldn't.
For what it's worth, I never turn off low power mode manually. It will eventually turn itself off, of course but having it on doesn't seem to interfere with standby mode.
Are you saying that it's not coming on at all? Every once in a while, I find it gets a bit flaky. What works then is if I make sure to lock the screen before putting it on charge.
Are you using the iPhone 13 your first post indicates? If so, that phone doesn't have an always on display. That means that even in Standby Mode, the screen will go dark. Nudging the phone or the nightstand should cause it to light up again.