chore(lint): partial apply docs code lints (#123)

cc @NtskwK ptal, and, some codes cannot pass the code lint, check plz.

## Summary by Sourcery

Apply linting and formatting updates across the docs app, and align
tooling and release config for the @dropout/docs package.

Enhancements:
- Normalize imports, string literals, and JSX formatting across the docs
app for consistent style and lint compliance.
- Tidy i18n, routing, and docs loader code without changing behavior,
improving readability and maintainability.

Build:
- Register the @dropout/docs package in the release/config system with
nodejs resolver and alpha pre-release tagging.
- Update docs-related Vite and TypeScript config files to match the new
linting and path conventions.
- Remove the nodejs publish command block from the shared changes config
to simplify release behavior.

Chores:
- Bump @biomejs/biome to the latest version and add core-js to
onlyBuiltDependencies for tooling compatibility.
- Add a changeset for @dropout/docs describing the docs linting patch
release.
- Introduce or update Biome and docs content metadata config files to
support the new linting setup.

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