Simplify ESPHome entity removal process

[bdraco]

Proposed change

Now that #110978 is fixed, we can remove most of entity removal code in ESPHome as deleting it from the registry will take care of removing the entity

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:
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
• Local tests pass. Your PR cannot be merged unless tests pass
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• Tests have been added to verify that the new code works.

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  Updated by running python3 -m script.gen_requirements_all.
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[home-assistant]

Hey there @OttoWinter, @jesserockz, @kbx81, mind taking a look at this pull request as it has been labeled with an integration (esphome) you are listed as a code owner for? Thanks!

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[bdraco]

functional retest is good.

Couldn't test it properly while traveling 😉