Backport PR #56980 on branch 2.2.x (WEB: Add version 2.2 to the dropdown) (#56983)

Backport PR #56980: WEB: Add version 2.2 to the dropdown

Co-authored-by: Thomas Li <47963215+lithomas1@users.noreply.github.com>

Author: meeseeksmachine

web/pandas/versions.json

@@ -5,11 +5,16 @@
         "url": "https://pandas.pydata.org/docs/dev/"
     },
     {
-        "name": "2.1 (stable)",
-        "version": "2.1",
+        "name": "2.2 (stable)",
+        "version": "2.2",
         "url": "https://pandas.pydata.org/docs/",
         "preferred": true
     },
+    {
+        "name": "2.1",
+        "version": "2.1",
+        "url": "https://pandas.pydata.org/pandas-docs/version/2.1/",
+    },
     {
         "name": "2.0",
         "version": "2.0",