website/docs: Update Docusaurus config. Prep for version picker. (#14401)

* website/docs: Clean up config. Add types.

* website/docs: Format MDX.

* website: Fix build warnings. Lint badges frontmatter.

website/docusaurus.config.cjs

@@ -0,0 +1,12 @@
+/**
+ * @file CommonJS Docusaurus config adapter.
+ *
+ * This exists to allow an ESM Docusaurus configuration to be imported in a CommonJS.
+ *
+ * @import Config from "./docusaurus.config.esm.mjs"
+ */
+
+/**
+ * @see {@linkcode Config} for the Docusaurus configuration type.
+ */
+module.exports = import("./docusaurus.config.esm.mjs").then(($) => $.default);