Upgrade rmcp to 3.0.0 (#36001)

## What changed

- Update the Rust MCP SDK from `3.0.0-beta.3` to `3.0.0` and adapt to its renamed metadata and server discovery types.
- Accept discovery responses without server identity metadata, using the configured server name as a fallback, and rely on the SDK's native support for namespaced server identity metadata.
- Preserve typed OAuth HTTP errors so transport failures, cross-origin redirects, and transient HTTP responses are reported instead of being treated as anonymous access.

## Testing

- Cover modern discovery with namespaced or missing server identity over HTTP, SSE, and stdio.
- Cover OAuth discovery error propagation for transport failures, redirects, and transient status codes.

GitOrigin-RevId: 12c1e45136cca89ce4fb15986c2b5df14608682a

codex-rs/codex-mcp/src/rmcp_client.rs

@@ -898,7 +898,8 @@ async fn start_server_task(
     )
     .await
     .map_err(StartupOutcomeError::from)?;
-    let server_info = mcp_server_info_from_implementation(initialize_result.server_info);
+    let server_info =
+        mcp_server_info_from_implementation(&server_name, initialize_result.server_info);
     let shared_tools = match (codex_apps_tools_cache_context.as_ref(), fetch_ticket) {
         (Some(cache_context), Some(fetch_ticket)) => cache_context.publish_if_newest_accepted(
             fetch_ticket,
@@ -954,7 +955,11 @@ fn mcp_initialize_request_params(
     .with_protocol_version(ProtocolVersion::V_2025_06_18)
 }
 
-fn mcp_server_info_from_implementation(server_info: Implementation) -> McpServerInfo {
+fn mcp_server_info_from_implementation(
+    server_name: &str,
+    server_info: Option<Implementation>,
+) -> McpServerInfo {
+    let server_info = server_info.unwrap_or_else(|| Implementation::new(server_name, ""));
     McpServerInfo {
         name: server_info.name,
         title: server_info.title,
@@ -1085,7 +1090,7 @@ mod tests {
     use super::*;
     use pretty_assertions::assert_eq;
     use rmcp::model::JsonObject;
-    use rmcp::model::Meta;
+    use rmcp::model::MetaObject;
     use rmcp::transport::auth::AuthError;
 
     #[test]
@@ -1098,6 +1103,44 @@ mod tests {
         assert!(error.is_authentication_required());
     }
 
+    #[test]
+    fn missing_server_implementation_uses_configured_server_name() {
+        assert_eq!(
+            mcp_server_info_from_implementation("configured-server", /*server_info*/ None),
+            McpServerInfo {
+                name: "configured-server".to_string(),
+                title: None,
+                version: String::new(),
+                description: None,
+                icons: None,
+                website_url: None,
+            }
+        );
+    }
+
+    #[test]
+    fn advertised_server_implementation_takes_precedence_over_configured_name() {
+        assert_eq!(
+            mcp_server_info_from_implementation(
+                "configured-server",
+                Some(
+                    Implementation::new("advertised-server", "1.2.3")
+                        .with_title("Advertised server")
+                        .with_description("Advertised description")
+                        .with_website_url("https://example.com"),
+                ),
+            ),
+            McpServerInfo {
+                name: "advertised-server".to_string(),
+                title: Some("Advertised server".to_string()),
+                version: "1.2.3".to_string(),
+                description: Some("Advertised description".to_string()),
+                icons: None,
+                website_url: Some("https://example.com".to_string()),
+            }
+        );
+    }
+
     #[test]
     fn mcp_initialize_advertises_openai_form_only_when_supported() {
         let unsupported = mcp_initialize_request_params(
@@ -1125,7 +1168,7 @@ mod tests {
             "test tool",
             Arc::new(JsonObject::default()),
         )
-        .with_meta(Meta(
+        .with_meta(MetaObject(
             serde_json::json!({
                 "connector_id": "connector_gmail",
                 "connector_name": "Gmail",