app-server: Return codex home in initialize response

codex-rs/app-server-protocol/schema/json/v1/InitializeResponse.json

@@ -1,6 +1,10 @@
 {
   "$schema": "http://json-schema.org/draft-07/schema#",
   "properties": {
+    "codexHome": {
+      "description": "Absolute path to the server's Codex home directory.",
+      "type": "string"
+    },
     "platformFamily": {
       "description": "Platform family for the running app-server target, for example `\"unix\"` or `\"windows\"`.",
       "type": "string"
@@ -14,6 +18,7 @@
     }
   },
   "required": [
+    "codexHome",
     "platformFamily",
     "platformOs",
     "userAgent"