feat: replace custom mcp-types crate with equivalents from rmcp (#10349)

We started working with MCP in Codex before
https://crates.io/crates/rmcp was mature, so we had our own crate for
MCP types that was generated from the MCP schema:


8b95d3e082/codex-rs/mcp-types/README.md

Now that `rmcp` is more mature, it makes more sense to use their MCP
types in Rust, as they handle details (like the `_meta` field) that our
custom version ignored. Though one advantage that our custom types had
is that our generated types implemented `JsonSchema` and `ts_rs::TS`,
whereas the types in `rmcp` do not. As such, part of the work of this PR
is leveraging the adapters between `rmcp` types and the serializable
types that are API for us (app server and MCP) introduced in #10356.

Note this PR results in a number of changes to
`codex-rs/app-server-protocol/schema`, which merit special attention
during review. We must ensure that these changes are still
backwards-compatible, which is possible because we have:

```diff
- export type CallToolResult = { content: Array<ContentBlock>, isError?: boolean, structuredContent?: JsonValue, };
+ export type CallToolResult = { content: Array<JsonValue>, structuredContent?: JsonValue, isError?: boolean, _meta?: JsonValue, };
```

so `ContentBlock` has been replaced with the more general `JsonValue`.
Note that `ContentBlock` was defined as:

```typescript
export type ContentBlock = TextContent | ImageContent | AudioContent | ResourceLink | EmbeddedResource;
```

so the deletion of those individual variants should not be a cause of
great concern.

Similarly, we have the following change in
`codex-rs/app-server-protocol/schema/typescript/Tool.ts`:

```
- export type Tool = { annotations?: ToolAnnotations, description?: string, inputSchema: ToolInputSchema, name: string, outputSchema?: ToolOutputSchema, title?: string, };
+ export type Tool = { name: string, title?: string, description?: string, inputSchema: JsonValue, outputSchema?: JsonValue, annotations?: JsonValue, icons?: Array<JsonValue>, _meta?: JsonValue, };
```

so:

- `annotations?: ToolAnnotations` ➡️ `JsonValue`
- `inputSchema: ToolInputSchema` ➡️ `JsonValue`
- `outputSchema?: ToolOutputSchema` ➡️ `JsonValue`

and two new fields: `icons?: Array<JsonValue>, _meta?: JsonValue`

---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/10349).
* #10357
* __->__ #10349
* #10356

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

@@ -7,24 +7,21 @@ use codex_core::protocol::FileChange;
 use codex_core::protocol::Op;
 use codex_core::protocol::ReviewDecision;
 use codex_protocol::ThreadId;
-use mcp_types::ElicitRequest;
-use mcp_types::ElicitRequestParamsRequestedSchema;
-use mcp_types::JSONRPCErrorError;
-use mcp_types::ModelContextProtocolRequest;
-use mcp_types::RequestId;
+use rmcp::model::ErrorData;
+use rmcp::model::RequestId;
 use serde::Deserialize;
 use serde::Serialize;
+use serde_json::Value;
 use serde_json::json;
 use tracing::error;
 
-use crate::codex_tool_runner::INVALID_PARAMS_ERROR_CODE;
 use crate::outgoing_message::OutgoingMessageSender;
 
 #[derive(Debug, Deserialize, Serialize)]
 pub struct PatchApprovalElicitRequestParams {
     pub message: String,
     #[serde(rename = "requestedSchema")]
-    pub requested_schema: ElicitRequestParamsRequestedSchema,
+    pub requested_schema: Value,
     #[serde(rename = "threadId")]
     pub thread_id: ThreadId,
     pub codex_elicitation: String,
@@ -64,11 +61,7 @@ pub(crate) async fn handle_patch_approval_request(
 
     let params = PatchApprovalElicitRequestParams {
         message: message_lines.join("\n"),
-        requested_schema: ElicitRequestParamsRequestedSchema {
-            r#type: "object".to_string(),
-            properties: json!({}),
-            required: None,
-        },
+        requested_schema: json!({"type":"object","properties":{}}),
         thread_id,
         codex_elicitation: "patch-approval".to_string(),
         codex_mcp_tool_call_id: tool_call_id.clone(),
@@ -85,14 +78,7 @@ pub(crate) async fn handle_patch_approval_request(
             error!("{message}");
 
             outgoing
-                .send_error(
-                    request_id.clone(),
-                    JSONRPCErrorError {
-                        code: INVALID_PARAMS_ERROR_CODE,
-                        message,
-                        data: None,
-                    },
-                )
+                .send_error(request_id.clone(), ErrorData::invalid_params(message, None))
                 .await;
 
             return;
@@ -100,7 +86,7 @@ pub(crate) async fn handle_patch_approval_request(
     };
 
     let on_response = outgoing
-        .send_request(ElicitRequest::METHOD, Some(params_json))
+        .send_request("elicitation/create", Some(params_json))
         .await;
 
     // Listen for the response on a separate task so we don't block the main agent loop.
@@ -115,7 +101,7 @@ pub(crate) async fn handle_patch_approval_request(
 
 pub(crate) async fn on_patch_approval_response(
     event_id: String,
-    receiver: tokio::sync::oneshot::Receiver<mcp_types::Result>,
+    receiver: tokio::sync::oneshot::Receiver<serde_json::Value>,
     codex: Arc<CodexThread>,
 ) {
     let response = receiver.await;