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.

website/tsconfig.json

@@ -0,0 +1,8 @@
+{
+    // This file is not used in compilation. It is here just for a nice editor experience.
+    "extends": "@docusaurus/tsconfig",
+    "compilerOptions": {
+        "baseUrl": "."
+    },
+    "exclude": [".docusaurus", "build", "node_modules"]
+}