My personal preference would be fairly simple:
-If one character is in turn-based mode, the whole world is in turn-based mode.
-Dialog is considered turn-based mode.
-If one character is in initiative, the whole world is in initiative.

It's a turn-based game. We can ignore that when wandering around and doing things that don't really care about timing. But as soon timing matters for a character, anyone or anything that could possibly affect them also needs to be on the clock.

I'm not suggesting that the UI needs to actively track every person in the world, but definitely all of the characters (wherever they are) should be in turn-based mode and any NPCs and monsters in the world that are not close enough to matter should default to stopping instead of continuing to walk around.