Well, um . . . thanks.
Firstly, the white wire on the single gang box switch which is hot may not always be hot depending on how the switches are thrown. One or the other traveler wire sin a three-way setup will always be hot.
I’m not going to suggest a solution here, but will pass on a couple observations. You would normally expect to see a black, white and red connected to a three way switch. Your switch in the two-gang box has two reds. But looking at the 2nd picture of that box, it looks like one of the reds is pigtailed to two blacks. That makes me wonder if the power is being fed to that switch via that pigtailed red, not to the light as we originally thought. (You would normally see a black pigtail to feed power.)
I’d pull the pigtailed red from the switch and see if it’s hot all the time. If it is, double-check to make sure it is attached to the black/dark screw on the switch, which is the common. If that’s good, then find the white bundled in the same three-wire containing the other two connections to that switch and see if it’s wire-nutted to other whites. If all that seems in order, then you may have power fed to the switch and a neutral in the box.
Here is the three-way switch FAQ:
When in doubt, consult with a licensed electrician.