chore: update from `eslint-plugin-markdown` to `@eslint/markdown` and use new rules

[pauliesnug]

Clear and concise description of the problem

ESLint just released v6.0.0 of eslint-plugin-markdown under @eslint/markdown and added new rules which currently wouldn't work based on the way we apply the markdown plugin (only used for codeblock linting).

Suggested solution

We could update to this new package and integrate Markdown fomatting and linting better. This might require changes to avoid conflicts between eslint-plugin-formatter's Markdown formatting and the new rules.

Alternative

No response

Additional context

No response

Validations

• [X] Follow our Code of Conduct
• [X] Read the Contributing Guide.
• [X] Check that there isn't already an issue that request the same feature to avoid creating a duplicate.