Migrate the Homebrew tap to grate-devs/homebrew-cask

## Context

Follow-up to #796. The grate cask currently lives in `erikbra/homebrew-cask` and is installed as `erikbra/cask/grate`. The canonical tap should be owned by the `grate-devs` organization.

## Scope

- Create or transfer the tap history to `grate-devs/homebrew-cask`.
- Publish the current grate cask as `grate-devs/cask/grate`.
- Provide a Homebrew-native migration from `erikbra/cask/grate`, using `tap_migrations.json` in the old tap if that is the selected approach.
- Update the cask to use canonical `grate-devs/grate` release URLs and the current documentation homepage.
- Configure cross-repository release automation using a narrowly scoped GitHub App or fine-grained token; the grate repository's `GITHUB_TOKEN` cannot write to another repository.
- Validate the cask on Apple Silicon and Intel.
- Add appropriate audit/syntax checks to the tap or release workflow.

## Acceptance criteria

- [ ] `brew install --cask grate-devs/cask/grate` succeeds.
- [ ] Both Apple Silicon and Intel downloads have correct checksums.
- [ ] Existing users of `erikbra/cask/grate` have a tested migration path.
- [ ] A stable grate release can update the organization-owned cask automatically.
- [ ] Prereleases do not update the stable cask.
- [ ] Cross-repository credentials are organization-manageable and least-privileged.
- [ ] Documentation changes are coordinated with the distribution documentation sweep.

## References

- #796
- Homebrew tap migrations: https://docs.brew.sh/Migrating-A-Formula-To-A-Tap
- GitHub repository transfers: https://docs.github.com/repositories/creating-and-managing-repositories/transferring-a-repository