Refactor MQTT discovery

[jbouwh]

Proposed change

• Move the discovery updater code for tag and device trigger to Mixins and make it an inheritable class.
• Use async_removed_from_device to filter the correct event to remove a device.
• Add a test for publishing an empty payload after device removal to align with the tag platform.
• deduplicate code for discovery in mixins.py

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New integration (thank you!)
• New feature (which adds functionality to an existing integration)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Additional information

• This PR fixes or closes issue: fixes #
• This PR is related to issue:
• Link to documentation pull request:

Checklist

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[probot-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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[emontnemery]

If this is not done, when does the loop of device registry updates happen?

[jbouwh]

Updated the comment to # Prevent a second cleanup round after the device is removed. Normally the device is cleaned up after an empty discovery payload. If the device is removed, all linked services are removed, that might cause multiple events. Only the first should trigger a cleanup.

[emontnemery]

Thanks a lot @jbouwh 👍