Fix triggerer race condition in HA setting

[Lioscro]

Fix triggerer race condition when there are multiple instances

closes: #38599

Detailed description is in the issue linked above. I was able to reproduce the issue in the latest main branch.

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[Lioscro]

Could have sworn I ran pre-commit already...

[Lioscro]

@uranusjr Thanks for the approval! I've taken all of your remaining suggestions. What is the process to getting this merged in?

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