## Why
Permission requests can originate in an environment whose path convention differs from the Codex host. Requiring the request working directory to be host-native prevents those requests from reaching interactive approval.
## What changed
- Carry the request `cwd` as a `LegacyAppPathString` through core events and the app-server protocol so the target environment's native representation is preserved.
- Convert the preserved value back to a `PathUri` when materializing permission grants.
- Regenerate the JSON and TypeScript protocol schemas for the updated `cwd` type.
## Testing
- Exercise the app-server permission request round trip with a target-native working directory across host path conventions.
- Verify remote permission requests retain their environment working directory and granted access still unblocks later execution.
GitOrigin-RevId: 97dc9707d9048883d20bab1b69c93871039f3188