Init cloud backup sync

[ludeeus]

Breaking change

Proposed change

Relies on #126122

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
• [ ] There is no commented out code in this PR.
• [ ] I have followed the development checklist
• [ ] I have followed the perfect PR recommendations
• [ ] The code has been formatted using Ruff (ruff format homeassistant tests)
• [ ] Tests have been added to verify that the new code works.

If user exposed functionality or configuration variables are added/changed:

• [ ] Documentation added/updated for www.home-assistant.io

If the code communicates with devices, web services, or third-party tools:

• [ ] The manifest file has all fields filled out correctly.
  Updated and included derived files by running: python3 -m script.hassfest.
• [ ] New or updated dependencies have been added to requirements_all.txt.
  Updated by running python3 -m script.gen_requirements_all.
• [ ] For the updated dependencies - a link to the changelog, or at minimum a diff between library versions is added to the PR description.

To help with the load of incoming pull requests:

• [ ] I have reviewed two other open pull requests in this repository.

[home-assistant[bot]]

Hey there @home-assistant/cloud, mind taking a look at this pull request as it has been labeled with an integration (cloud) you are listed as a code owner for? Thanks!

Code owner commands

Code owners of `cloud` can trigger bot actions by commenting: - `@home-assistant close` Closes the pull request. - `@home-assistant rename Awesome new title` Renames the pull request. - `@home-assistant reopen` Reopen the pull request. - `@home-assistant unassign cloud` Removes the current integration label and assignees on the pull request, add the integration domain after the command. - `@home-assistant add-label needs-more-information` Add a label (needs-more-information, problem in dependency, problem in custom component) to the pull request. - `@home-assistant remove-label needs-more-information` Remove a label (needs-more-information, problem in dependency, problem in custom component) on the pull request.