Restore entity ID and user customizations of deleted entities

[emontnemery]

Proposed change

Keep and restore entity ID and user customizations of aliases, area_id, categories, device_class, disabled_by, hidden_by, icon, labels, name and options when restoring deleted entities

If the area_id no longer exists, it will not be restored
Any category or label which no longer exists will not be restored

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:
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• Link to developer documentation pull request:
• Link to frontend pull request:

Checklist

• The code change is tested and works locally.
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• The code has been formatted using Ruff (ruff format homeassistant tests)
• Tests have been added to verify that the new code works.

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[emontnemery]

Tests are failing because integrations expect entity ID to not be stable when an entity is removed and then added back with a changed name.

[emontnemery]

Maybe we should always restore disabled_by and hidden_by flags, also if the integration has changed?
That would match the behavior for live entities (we never change the disabled or hidden flags for an entity which has already been seen).