Add background prefix compaction prewarm

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

@@ -3652,6 +3652,16 @@
       "$schema": "http://json-schema.org/draft-07/schema#",
       "description": "Deprecated: Use `ContextCompaction` item type instead.",
       "properties": {
+        "kind": {
+          "anyOf": [
+            {
+              "$ref": "#/definitions/ContextCompactionKind"
+            },
+            {
+              "type": "null"
+            }
+          ]
+        },
         "threadId": {
           "type": "string"
         },
@@ -3666,6 +3676,13 @@
       "title": "ContextCompactedNotification",
       "type": "object"
     },
+    "ContextCompactionKind": {
+      "enum": [
+        "classic",
+        "prefix"
+      ],
+      "type": "string"
+    },
     "CreditsSnapshot": {
       "properties": {
         "balance": {
@@ -11218,6 +11235,16 @@
             "id": {
               "type": "string"
             },
+            "kind": {
+              "anyOf": [
+                {
+                  "$ref": "#/definitions/ContextCompactionKind"
+                },
+                {
+                  "type": "null"
+                }
+              ]
+            },
             "type": {
               "enum": [
                 "contextCompaction"