Add experimental context management activation (#42385)

## What changed

- Add the under-development `features.context_management.experimental_mode` configuration and schema.
- For eligible ChatGPT Plus, Pro, and Pro Lite sessions using the Codex backend, enable token-budget context, history notes, and the `new_context` tool when experimental context management is configured.
- Keep the feature disabled for custom providers, provider credentials, non-Codex endpoints, and temporary structured threads.

## Testing

- Cover subscription eligibility, backend restrictions, configuration resolution, token-budget guidance, and temporary-thread overrides.

GitOrigin-RevId: 19402af19c4d69e09a7cdb3687ee7d233f6a562a

codex-rs/core/config.schema.json

@@ -699,6 +699,9 @@
             "content_item_kinds": {
               "type": "boolean"
             },
+            "context_management": {
+              "$ref": "#/definitions/FeatureToml_for_ContextManagementConfigToml"
+            },
             "current_time_reminder": {
               "$ref": "#/definitions/FeatureToml_for_CurrentTimeReminderConfigToml"
             },
@@ -1142,6 +1145,16 @@
       },
       "type": "object"
     },
+    "ContextManagementConfigToml": {
+      "additionalProperties": false,
+      "properties": {
+        "experimental_mode": {
+          "description": "Enables experimental context management.",
+          "type": "boolean"
+        }
+      },
+      "type": "object"
+    },
     "CurrentTimeReminderConfigToml": {
       "additionalProperties": false,
       "properties": {
@@ -1255,6 +1268,16 @@
         }
       ]
     },
+    "FeatureToml_for_ContextManagementConfigToml": {
+      "anyOf": [
+        {
+          "type": "boolean"
+        },
+        {
+          "$ref": "#/definitions/ContextManagementConfigToml"
+        }
+      ]
+    },
     "FeatureToml_for_CurrentTimeReminderConfigToml": {
       "anyOf": [
         {
@@ -6014,6 +6037,9 @@
         "content_item_kinds": {
           "type": "boolean"
         },
+        "context_management": {
+          "$ref": "#/definitions/FeatureToml_for_ContextManagementConfigToml"
+        },
         "current_time_reminder": {
           "$ref": "#/definitions/FeatureToml_for_CurrentTimeReminderConfigToml"
         },