Specific to Waukeen's Rest, the issue is generally presentation/trigger. The timer/time progression is a valid, but also bigger discussion (i.e. time progressing with day/night cycle vs. long rests) - but within the current system the major issue is a lack of a "before, during, and after" states for the burning area.
I.e. the most simple solution is to ensure the fire isn't visible super far away, and but once it becomes anywhere close to visible, the quest and timer starts (and the player should be warned by the journal at this time). And once the timer completes or the quest is completed, then we just need a end slate for the inn to stay in (i.e. completely burnt, etc).
For better or for worst, BG3 has "timed/urgent" quests. They aren't triggered by the actual passage of time but progression/long rests, but they are urgent none the less in the sense that they're missable if you progressed too far.
I.e. saving the child from the Harpy, saving that tiefling girl from the bugbear assassin, the fire at Waukeen's Rest, Nere's quest at Grymforge, etc.
