Use ConversationId instead of raw Uuids (#3282)

We're trying to migrate from `session_id: Uuid` to `conversation_id:
ConversationId`. Not only does this give us more type safety but it
unifies our terminology across Codex and with the implementation of
session resuming, a conversation (which can span multiple sessions) is
more appropriate.

I started this impl on https://github.com/openai/codex/pull/3219 as part
of getting resume working in the extension but it's big enough that it
should be broken out.

codex-rs/mcp-server/src/codex_tool_config.rs

@@ -181,8 +181,8 @@ impl CodexToolCallParam {
 #[derive(Debug, Clone, Serialize, Deserialize, JsonSchema)]
 #[serde(rename_all = "camelCase")]
 pub struct CodexToolCallReplyParam {
-    /// The *session id* for this conversation.
-    pub session_id: String,
+    /// The conversation id for this Codex session.
+    pub conversation_id: String,
 
     /// The *next user prompt* to continue the Codex conversation.
     pub prompt: String,
@@ -213,7 +213,8 @@ pub(crate) fn create_tool_for_codex_tool_call_reply_param() -> Tool {
         input_schema: tool_input_schema,
         output_schema: None,
         description: Some(
-            "Continue a Codex session by providing the session id and prompt.".to_string(),
+            "Continue a Codex conversation by providing the conversation id and prompt."
+                .to_string(),
         ),
         annotations: None,
     }
@@ -308,21 +309,21 @@ mod tests {
         let tool = create_tool_for_codex_tool_call_reply_param();
         let tool_json = serde_json::to_value(&tool).expect("tool serializes");
         let expected_tool_json = serde_json::json!({
-          "description": "Continue a Codex session by providing the session id and prompt.",
+          "description": "Continue a Codex conversation by providing the conversation id and prompt.",
           "inputSchema": {
             "properties": {
+              "conversationId": {
+                "description": "The conversation id for this Codex session.",
+                "type": "string"
+              },
               "prompt": {
                 "description": "The *next user prompt* to continue the Codex conversation.",
                 "type": "string"
               },
-              "sessionId": {
-                "description": "The *session id* for this conversation.",
-                "type": "string"
-              },
             },
             "required": [
+              "conversationId",
               "prompt",
-              "sessionId",
             ],
             "type": "object",
           },