Make fuzzy file search case insensitive (#15772)

Makes fuzzy file search use case-insensitive matching instead of
smart-case in `codex-file-search`. I find smart-case to be a poor user
experience -using the wrong case for a letter drops its match so
significantly, it often drops off the results list, effectively making a
search case-sensitive.

codex-rs/app-server/tests/suite/fuzzy_file_search.rs

@@ -366,6 +366,30 @@ async fn test_fuzzy_file_search_session_streams_updates() -> Result<()> {
     Ok(())
 }
 
+#[tokio::test(flavor = "multi_thread", worker_threads = 2)]
+async fn test_fuzzy_file_search_session_update_is_case_insensitive() -> Result<()> {
+    let codex_home = TempDir::new()?;
+    let root = TempDir::new()?;
+    std::fs::write(root.path().join("alpha.txt"), "contents")?;
+    let mut mcp = initialized_mcp(&codex_home).await?;
+
+    let root_path = root.path().to_string_lossy().to_string();
+    let session_id = "session-case-insensitive";
+
+    mcp.start_fuzzy_file_search_session(session_id, vec![root_path.clone()])
+        .await?;
+    mcp.update_fuzzy_file_search_session(session_id, "ALP")
+        .await?;
+
+    let payload =
+        wait_for_session_updated(&mut mcp, session_id, "ALP", FileExpectation::NonEmpty).await?;
+    assert_eq!(payload.files.len(), 1);
+    assert_eq!(payload.files[0].root, root_path);
+    assert_eq!(payload.files[0].path, "alpha.txt");
+
+    Ok(())
+}
+
 #[tokio::test(flavor = "multi_thread", worker_threads = 2)]
 async fn test_fuzzy_file_search_session_no_updates_after_complete_until_query_edited() -> Result<()>
 {