Prepare 0.1.0-beta.4 release

[HPaulson]

Summary

• Update release metadata to 0.1.0-beta.4 across the package, Home Assistant integration/app, and Docker image.
• Fix README branding for published repository and HACS package views.
• Avoid duplicate CI runs after changes land on main.

Validation

• pnpm ci:check
• Formatting, typecheck, lint, 69 tests, and build.
• Docker build and authenticated API smoke test.

Release

After merge, tag the resulting main commit as v0.1.0-beta.4.