Attempt to make the monarch more thread safe. (#11189)

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## Summary of the Pull Request

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## References
#11083 
#11143 

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## PR Checklist
* [ ] Closes #xxx
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* [ ] Schema updated.
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## Detailed Description of the Pull Request / Additional comments
While testing the save/quit features a number of issues were found that were caused by poor synchronization on the monarch, resulting in various unexpected crashes. Because this uses std collections, and I didn't see any builtin winrt multithreaded containers I went with the somewhat heavy-handed mutex approach.

e.g. 
- #11083 (comment)
- #11083 (comment)
- #11143

This also makes it so that on quit peasants don't try to become the monarch, and the monarch closes their peasant last to prevent elections from happening.

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## Validation Steps Performed
Create many windows (hold down ctrl-shift-n) then use the quit action from peasants/the monarch to make sure everything closes properly.