Wire realtime api to core (#12268)

- Introduce `RealtimeConversationManager` for realtime API management 
- Add `op::conversation` to start conversation, insert audio, insert
text, and close conversation.
- emit conversation lifecycle and realtime events.
- Move shared realtime payload types into codex-protocol and add core
e2e websocket tests for start/replace/transport-close paths.

Things to consider:
- Should we use the same `op::` and `Events` channel to carry audio? I
think we should try this simple approach and later we can create
separate one if the channels got congested.
- Sending text updates to the client: we can start simple and later
restrict that.
- Provider auth isn't wired for now intentionally

codex-rs/app-server-protocol/schema/json/ServerNotification.json

@@ -1372,6 +1372,73 @@
           "title": "WarningEventMsg",
           "type": "object"
         },
+        {
+          "description": "Realtime conversation lifecycle start event.",
+          "properties": {
+            "session_id": {
+              "type": [
+                "string",
+                "null"
+              ]
+            },
+            "type": {
+              "enum": [
+                "realtime_conversation_started"
+              ],
+              "title": "RealtimeConversationStartedEventMsgType",
+              "type": "string"
+            }
+          },
+          "required": [
+            "type"
+          ],
+          "title": "RealtimeConversationStartedEventMsg",
+          "type": "object"
+        },
+        {
+          "description": "Realtime conversation streaming payload event.",
+          "properties": {
+            "payload": {
+              "$ref": "#/definitions/RealtimeEvent"
+            },
+            "type": {
+              "enum": [
+                "realtime_conversation_realtime"
+              ],
+              "title": "RealtimeConversationRealtimeEventMsgType",
+              "type": "string"
+            }
+          },
+          "required": [
+            "payload",
+            "type"
+          ],
+          "title": "RealtimeConversationRealtimeEventMsg",
+          "type": "object"
+        },
+        {
+          "description": "Realtime conversation lifecycle close event.",
+          "properties": {
+            "reason": {
+              "type": [
+                "string",
+                "null"
+              ]
+            },
+            "type": {
+              "enum": [
+                "realtime_conversation_closed"
+              ],
+              "title": "RealtimeConversationClosedEventMsgType",
+              "type": "string"
+            }
+          },
+          "required": [
+            "type"
+          ],
+          "title": "RealtimeConversationClosedEventMsg",
+          "type": "object"
+        },
         {
           "description": "Model routing changed from the requested model to a different model.",
           "properties": {
@@ -5176,6 +5243,120 @@
         }
       ]
     },
+    "RealtimeAudioFrame": {
+      "properties": {
+        "data": {
+          "type": "string"
+        },
+        "num_channels": {
+          "format": "uint16",
+          "minimum": 0.0,
+          "type": "integer"
+        },
+        "sample_rate": {
+          "format": "uint32",
+          "minimum": 0.0,
+          "type": "integer"
+        },
+        "samples_per_channel": {
+          "format": "uint32",
+          "minimum": 0.0,
+          "type": [
+            "integer",
+            "null"
+          ]
+        }
+      },
+      "required": [
+        "data",
+        "num_channels",
+        "sample_rate"
+      ],
+      "type": "object"
+    },
+    "RealtimeEvent": {
+      "oneOf": [
+        {
+          "additionalProperties": false,
+          "properties": {
+            "SessionCreated": {
+              "properties": {
+                "session_id": {
+                  "type": "string"
+                }
+              },
+              "required": [
+                "session_id"
+              ],
+              "type": "object"
+            }
+          },
+          "required": [
+            "SessionCreated"
+          ],
+          "title": "SessionCreatedRealtimeEvent",
+          "type": "object"
+        },
+        {
+          "additionalProperties": false,
+          "properties": {
+            "SessionUpdated": {
+              "properties": {
+                "backend_prompt": {
+                  "type": [
+                    "string",
+                    "null"
+                  ]
+                }
+              },
+              "type": "object"
+            }
+          },
+          "required": [
+            "SessionUpdated"
+          ],
+          "title": "SessionUpdatedRealtimeEvent",
+          "type": "object"
+        },
+        {
+          "additionalProperties": false,
+          "properties": {
+            "AudioOut": {
+              "$ref": "#/definitions/RealtimeAudioFrame"
+            }
+          },
+          "required": [
+            "AudioOut"
+          ],
+          "title": "AudioOutRealtimeEvent",
+          "type": "object"
+        },
+        {
+          "additionalProperties": false,
+          "properties": {
+            "ConversationItemAdded": true
+          },
+          "required": [
+            "ConversationItemAdded"
+          ],
+          "title": "ConversationItemAddedRealtimeEvent",
+          "type": "object"
+        },
+        {
+          "additionalProperties": false,
+          "properties": {
+            "Error": {
+              "type": "string"
+            }
+          },
+          "required": [
+            "Error"
+          ],
+          "title": "ErrorRealtimeEvent",
+          "type": "object"
+        }
+      ]
+    },
     "ReasoningEffort": {
       "description": "See https://platform.openai.com/docs/guides/reasoning?api-mode=responses#get-started-with-reasoning",
       "enum": [