Add linting for markdown files (#3646)

I also reworked the Linters section in `CONTRIBUTING.md` a bit and
switched the `prettier` config to a flat config.

Co-authored-by: Veeck <github@veeck.de>

.github/CONTRIBUTING.md

@@ -6,22 +6,28 @@ We hold our code to standard, and these standards are documented below.
 
 ## Linters
 
-We use prettier for automatic linting of all our files: `npm run lint:prettier`.
+We use [prettier](https://prettier.io/) for automatic formatting a lot all our files. The configuration is in our `prettier.config.mjs` file.
+
+To run prettier, use `npm run lint:prettier`.
 
 ### JavaScript: Run ESLint
 
-We use [ESLint](https://eslint.org) on our JavaScript files.
-
-The ESLint configuration is in our `eslint.config.mjs` file.
+We use [ESLint](https://eslint.org) to lint our JavaScript files. The configuration is in our `eslint.config.mjs` file.
 
 To run ESLint, use `npm run lint:js`.
 
 ### CSS: Run StyleLint
 
-We use [StyleLint](https://stylelint.io) to lint our CSS. Our configuration is in our `.stylelintrc` file.
+We use [StyleLint](https://stylelint.io) to lint our CSS. The configuration is in our `.stylelintrc.json` file.
 
 To run StyleLint, use `npm run lint:css`.
 
+### Markdown: Run markdownlint
+
+We use [markdownlint-cli2](https://github.com/DavidAnson/markdownlint-cli2) to lint our markdown files. The configuration is in our `.markdownlint.json` file.
+
+To run markdownlint, use `npm run markdownlint:css`.
+
 ## Testing
 
 We use [Jest](https://jestjs.io) for JavaScript testing.

.github/workflows/automated-tests.yaml

@@ -39,4 +39,5 @@ jobs:
           npm run test:prettier
           npm run test:js
           npm run test:css
+          npm run test:markdown
           npm run test