chore: upgrade Node.js from 20.19.4 to 22.19.0 and update dependencies (#19870)

# Update Node.js from 20.19.4 to 22.19.0

This PR updates Node.js from v20.19.4 to v22.19.0 across the codebase. The change includes:

- Updated Node.js version in GitHub Actions setup-node workflow
- Updated Node.js version in the dogfood Dockerfile
- Changed from `pkgs.nodejs_20` to `unstablePkgs.nodejs_22` in the Nix flake
- Updated the Node.js engine version constraints in package.json files to allow Node.js 22
- Updated Playwright from v1.47.0 to v1.50.1
- Updated tzdata dependency from v1.0.44 to v1.0.46
- Updated the flake.lock file with latest nixpkgs references

The PR also improves the error message for Playwright version mismatches by showing the actual versions in the error.

.github/actions/setup-node/action.yaml

@@ -16,7 +16,7 @@ runs:
     - name: Setup Node
       uses: actions/setup-node@0a44ba7841725637a19e28fa30b79a866c81b0a6 # v4.0.4
       with:
-        node-version: 20.19.4
+        node-version: 22.19.0
         # See https://github.com/actions/setup-node#caching-global-packages-data
         cache: "pnpm"
         cache-dependency-path: ${{ inputs.directory }}/pnpm-lock.yaml