Presentation state can go out of sync

**To Reproduce**
Steps to reproduce the behavior:
1. Play a presentation
2. Switch to another doc
3. Play that one
4. the one you started first now has a non-functional "stop" button in the toolbar.

Reproduce the sequence in the issue: play one presentation, switch to another document, play it, then inspect the first document's toolbar. Trace how presentation and stop-button state changes across the document switch. Done means the first presentation's stop button remains functional or is correctly reset after another document starts playing.

Written by the indexing model from the issue text.