Fix race on check MQTT subscriptions

[jbouwh]

Proposed change

Check MQTT subscriptions under paho client lock to avoid a race.

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• This PR fixes or closes issue: fixes #
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[home-assistant]

Hey there @emontnemery, mind taking a look at this pull request as it has been labeled with an integration (mqtt) you are listed as a code owner for? Thanks!

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[corporategoth]

This is missing a key thing that is in #88072

Specifically, when you subscribe to a topic, MQTT will send you the latest status for that topic.
For the initial subscription, this will work (and the entity will get notified of that).

My change also adds a last_message for each topic (at least each simple topic) and will send the last message that was received on that topic to new subscribers.

[corporategoth]

Though, I guess, we will now have to change my MR to accommodate this MR since it's merged.

[corporategoth]

Nevermind, I mis-read. The other only handles unsubscribes, not subscribes. My MR is still relevant.