website: Use Docusaurus Frontmatter for badges (#12893)

website/docs: Reduce redundant usage of badges. Move badge logic to components.

- Fix JSX class name warning.
- Remove duplicate titles.
- Flesh out `support_level` frontmatter.

web/src/global.d.ts

@@ -6,6 +6,12 @@ declare module "*.md" {
     const filename: string;
 }
 
+declare module "*.mdx" {
+    const html: string;
+    const metadata: { [key: string]: string };
+    const filename: string;
+}
+
 declare namespace Intl {
     class ListFormat {
         constructor(locale: string, args: { [key: string]: string });