[codex] Migrate apply_patch to executor filesystem (#17027)

- Migrate apply-patch verification and application internals to use the
async `ExecutorFileSystem` abstraction from `exec-server`.
- Convert apply-patch `cwd` handling to `AbsolutePathBuf` through the
verifier/parser/handler boundary.

Doesn't change how the tool itself works.

codex-rs/apply-patch/src/standalone_executable.rs

@@ -48,7 +48,30 @@ pub fn run_main() -> i32 {
 
     let mut stdout = std::io::stdout();
     let mut stderr = std::io::stderr();
-    match crate::apply_patch(&patch_arg, &mut stdout, &mut stderr) {
+    let cwd = match codex_utils_absolute_path::AbsolutePathBuf::current_dir() {
+        Ok(cwd) => cwd,
+        Err(err) => {
+            eprintln!("Error: Failed to determine current directory.\n{err}");
+            return 1;
+        }
+    };
+    let runtime = match tokio::runtime::Builder::new_current_thread()
+        .enable_all()
+        .build()
+    {
+        Ok(runtime) => runtime,
+        Err(err) => {
+            eprintln!("Error: Failed to initialize runtime.\n{err}");
+            return 1;
+        }
+    };
+    match runtime.block_on(crate::apply_patch(
+        &patch_arg,
+        &cwd,
+        &mut stdout,
+        &mut stderr,
+        codex_exec_server::LOCAL_FS.as_ref(),
+    )) {
         Ok(()) => {
             // Flush to ensure output ordering when used in pipelines.
             let _ = stdout.flush();