[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/exec-server/tests/file_system.rs

@@ -122,6 +122,12 @@ async fn file_system_methods_cover_surface_area(use_remote: bool) -> Result<()>
         .with_context(|| format!("mode={use_remote}"))?;
     assert_eq!(nested_file_contents, b"hello from trait");
 
+    let nested_file_text = file_system
+        .read_file_text(&absolute_path(nested_file.clone()))
+        .await
+        .with_context(|| format!("mode={use_remote}"))?;
+    assert_eq!(nested_file_text, "hello from trait");
+
     file_system
         .copy(
             &absolute_path(nested_file),