Trigger auto-update throuogh Core service call

[agners]

Proposed change

Instead of auto-updating add-ons on Supervisor side trigger an update through Core via a WebSocket service call. This makes sure that the backup is categorized correctly and all backup features like retention are applied.

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (which adds functionality to the supervisor)
• 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:
• Link to cli pull request:
• Link to client library pull request:

Checklist

• The code change is tested and works locally.
• Local tests pass. Your PR cannot be merged unless tests pass
• There is no commented out code in this PR.
• I have followed the development checklist
• The code has been formatted using Ruff (ruff format supervisor tests)
• Tests have been added to verify that the new code works.

If API endpoints or add-on configuration are added/changed:

• Documentation added/updated for developers.home-assistant.io
• CLI updated (if necessary)
• Client library updated (if necessary)

[agners]

This breaks if users rename the add-on update entities.

To me, it seems rather brittle to call Core here.

What I'd suggest is to extend the SupervisorAddonUpdateEntity class in Core instead. We are missing the breaking version info currently, but that can be added. Since we ultimately like to have auto-updating entities on Core end this seems like the right direction to me.