fix(theme): sync package manager code group tabs

[L-1ngg]

Summary

Sync package manager code-group tabs across docs pages.

VitePress code groups manage tab state locally, so selecting pnpm or bun in one command group does not update
other package-manager command groups on the same page. This adds a small client-side theme hook that syncs only
package manager tabs: npm, yarn, pnpm, bun, and deno.

Runtime tabs such as Deno, Bun, Node.js, and platform tabs such as Cloudflare Workers are intentionally not
synced.

If a selected package manager tab is not available in another code group, that code group is left unchanged.

Verification

• bun install --frozen-lockfile
• bun x prettier --check .vitepress/theme/index.ts .vitepress/theme/use-synced-package-manager-code-groups.ts
• bun run format
• bun run build

[yusukebe]

LGTM!

[yusukebe]

Hey @L-1ngg

Awesome! It will be helpful. Thank you for the contribution!