Add thread section management APIs (#36380)

## What changed

- Add `threadSection/create`, `threadSection/update`, and `threadSection/delete` app-server methods, with generated protocol schemas and TypeScript bindings.
- Persist custom sections in SQLite with stable UUIDv7 identities, trim and validate display names, and prevent renaming or deleting the built-in pinned section.
- Delete sections transactionally and return their active and archived threads to the unsectioned list.
- Serialize section mutations with section listing so concurrent requests observe ordered updates.

## Testing

- Cover section persistence across restarts, ordered renames, member cleanup on deletion, invalid requests, unsupported stores, and thread-store/state-runtime behavior.

GitOrigin-RevId: dc9a4be283c21dbc93ab1829eafc4825d8df6575

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.v2.schemas.json

@@ -1834,6 +1834,78 @@
           "title": "ThreadSection/listRequest",
           "type": "object"
         },
+        {
+          "properties": {
+            "id": {
+              "$ref": "#/definitions/RequestId"
+            },
+            "method": {
+              "enum": [
+                "threadSection/create"
+              ],
+              "title": "ThreadSection/createRequestMethod",
+              "type": "string"
+            },
+            "params": {
+              "$ref": "#/definitions/ThreadSectionCreateParams"
+            }
+          },
+          "required": [
+            "id",
+            "method",
+            "params"
+          ],
+          "title": "ThreadSection/createRequest",
+          "type": "object"
+        },
+        {
+          "properties": {
+            "id": {
+              "$ref": "#/definitions/RequestId"
+            },
+            "method": {
+              "enum": [
+                "threadSection/update"
+              ],
+              "title": "ThreadSection/updateRequestMethod",
+              "type": "string"
+            },
+            "params": {
+              "$ref": "#/definitions/ThreadSectionUpdateParams"
+            }
+          },
+          "required": [
+            "id",
+            "method",
+            "params"
+          ],
+          "title": "ThreadSection/updateRequest",
+          "type": "object"
+        },
+        {
+          "properties": {
+            "id": {
+              "$ref": "#/definitions/RequestId"
+            },
+            "method": {
+              "enum": [
+                "threadSection/delete"
+              ],
+              "title": "ThreadSection/deleteRequestMethod",
+              "type": "string"
+            },
+            "params": {
+              "$ref": "#/definitions/ThreadSectionDeleteParams"
+            }
+          },
+          "required": [
+            "id",
+            "method",
+            "params"
+          ],
+          "title": "ThreadSection/deleteRequest",
+          "type": "object"
+        },
         {
           "properties": {
             "id": {
@@ -18357,6 +18429,56 @@
       ],
       "type": "object"
     },
+    "ThreadSectionCreateParams": {
+      "$schema": "http://json-schema.org/draft-07/schema#",
+      "description": "Parameters for creating an independently persisted thread section.",
+      "properties": {
+        "name": {
+          "description": "The user-visible name of the section.",
+          "type": "string"
+        }
+      },
+      "required": [
+        "name"
+      ],
+      "title": "ThreadSectionCreateParams",
+      "type": "object"
+    },
+    "ThreadSectionCreateResponse": {
+      "$schema": "http://json-schema.org/draft-07/schema#",
+      "description": "The independently persisted section created by the server.",
+      "properties": {
+        "section": {
+          "$ref": "#/definitions/ThreadSection"
+        }
+      },
+      "required": [
+        "section"
+      ],
+      "title": "ThreadSectionCreateResponse",
+      "type": "object"
+    },
+    "ThreadSectionDeleteParams": {
+      "$schema": "http://json-schema.org/draft-07/schema#",
+      "description": "Parameters for deleting an independently persisted thread section.",
+      "properties": {
+        "sectionId": {
+          "description": "The stable, server-generated identity of the section to delete.",
+          "type": "string"
+        }
+      },
+      "required": [
+        "sectionId"
+      ],
+      "title": "ThreadSectionDeleteParams",
+      "type": "object"
+    },
+    "ThreadSectionDeleteResponse": {
+      "$schema": "http://json-schema.org/draft-07/schema#",
+      "description": "Successful deletion does not return additional section data.",
+      "title": "ThreadSectionDeleteResponse",
+      "type": "object"
+    },
     "ThreadSectionListParams": {
       "$schema": "http://json-schema.org/draft-07/schema#",
       "description": "Parameters for listing independently persisted thread sections.",
@@ -18440,6 +18562,40 @@
       "title": "ThreadSectionMoveResponse",
       "type": "object"
     },
+    "ThreadSectionUpdateParams": {
+      "$schema": "http://json-schema.org/draft-07/schema#",
+      "description": "Parameters for updating an independently persisted thread section.",
+      "properties": {
+        "name": {
+          "description": "The updated user-visible name of the section.",
+          "type": "string"
+        },
+        "sectionId": {
+          "description": "The stable, server-generated identity of the section to update.",
+          "type": "string"
+        }
+      },
+      "required": [
+        "name",
+        "sectionId"
+      ],
+      "title": "ThreadSectionUpdateParams",
+      "type": "object"
+    },
+    "ThreadSectionUpdateResponse": {
+      "$schema": "http://json-schema.org/draft-07/schema#",
+      "description": "The independently persisted section after its name is updated.",
+      "properties": {
+        "section": {
+          "$ref": "#/definitions/ThreadSection"
+        }
+      },
+      "required": [
+        "section"
+      ],
+      "title": "ThreadSectionUpdateResponse",
+      "type": "object"
+    },
     "ThreadSetNameParams": {
       "$schema": "http://json-schema.org/draft-07/schema#",
       "properties": {