Let MQTT availability for snips be managed by dependencies

[jbouwh]

Proposed change

Since #81733 the snips integration has been leaning on checks if MQTT was started up. Since HA should manage the dependencies for integrations, (improvements were made with #91454) it should be safe now now to re move the check for MQTT availability and waiting for mqtt te become available.

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)
• Deprecation (breaking change to happen in the future)
• 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: Component Snips can’t subscribe to MQTT at startup #81431
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
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• Tests have been added to verify that the new code works.

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