Add API docs link checker script and fix broken API links

[dobromirts]

1. Adds scripts/check-api-links.mjs - a CLI tool that scans built HTML output for staging API links and verifies each one against the live TypeDoc site
2. Fixes broken API links across Blazor EN/JP, React EN, and Angular EN/JP by correcting type kinds (interface/class/type/enum), platform prefixes, and wrong package mappings
3. Adds dockmanager package entry to React's apiPackages in platform-context.ts so all DockManager-related links resolve to the correct igniteui-react-dockmanager package

How the checker works:

The script scans compiled HTML in the dist/ folder, extracts all staging API URLs, resolves each package to its latest versioned URL, and fetches them concurrently. It distinguishes between HTTP errors (server/network failures) and TypeDoc "NOT FOUND" responses (valid HTTP 200 but missing type/member).

Usage
Build the platform(s) you want to check (both EN and JP are included automatically per platform):

npm run angular:build-staging # builds angular + angular-jp
npm run react:build-staging # builds react + react-jp
Run the checker and generate a Markdown report:

npm run check-api-links:report:angular
npm run check-api-links:report:react
npm run check-api-links:report:blazor
Reports are written to api-link-report-.md in the repo root.