[mcp-server] Expose fuzzy file search in MCP (#2677)

## Summary
Expose a simple fuzzy file search implementation for mcp clients to work
with

## Testing
- [x] Tested locally

codex-rs/protocol/src/mcp_protocol.rs

@@ -184,6 +184,11 @@ pub enum ClientRequest {
         #[serde(rename = "id")]
         request_id: RequestId,
     },
+    FuzzyFileSearch {
+        #[serde(rename = "id")]
+        request_id: RequestId,
+        params: FuzzyFileSearchParams,
+    },
     /// Execute a command (argv vector) under the server's sandbox.
     ExecOneOffCommand {
         #[serde(rename = "id")]
@@ -662,6 +667,32 @@ pub struct ApplyPatchApprovalResponse {
     pub decision: ReviewDecision,
 }
 
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, TS)]
+#[serde(rename_all = "camelCase")]
+#[ts(rename_all = "camelCase")]
+pub struct FuzzyFileSearchParams {
+    pub query: String,
+    pub roots: Vec<String>,
+    // if provided, will cancel any previous request that used the same value
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub cancellation_token: Option<String>,
+}
+
+/// Superset of [`codex_file_search::FileMatch`]
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, TS)]
+pub struct FuzzyFileSearchResult {
+    pub root: String,
+    pub path: String,
+    pub score: u32,
+    #[serde(skip_serializing_if = "Option::is_none")]
+    pub indices: Option<Vec<u32>>,
+}
+
+#[derive(Serialize, Deserialize, Debug, Clone, PartialEq, TS)]
+pub struct FuzzyFileSearchResponse {
+    pub files: Vec<FuzzyFileSearchResult>,
+}
+
 #[derive(Serialize, Deserialize, Debug, Clone, PartialEq, TS)]
 #[serde(rename_all = "camelCase")]
 pub struct LoginChatGptCompleteNotification {