[FR]: Investigate using `markdown-link-check` action in GHA infra

### Description

Broken links are easy to miss when adding and editing markdown files. The [`markdown-link-check`](https://github.com/marketplace/actions/markdown-link-check) checks for broken links.

Steps
1. Add a `markdown.yml` workflow that runs on triggers on changes to any `*.md` files in the repo.
2. Add `markdown-link-check` check to added workflow file.

### API Proposal

_No response_

### Firebase Product(s)

N/A

Start by reviewing the repository's existing GitHub Actions workflows, then create the requested markdown.yml workflow. Configure it for changes to *.md files and use markdown-link-check; done means the workflow runs successfully and detects broken Markdown links.

Written by the indexing model from the issue text.