Fix empty rollout path app-server handling (#23400)

## Summary
- Coerce `path: ""` to `None` at the v2 protocol params deserialization
boundary for `thread/resume` and `thread/fork`.
- Restore the pre-ThreadStore running-thread resume behavior: if
`threadId` is already running, rejoin it by id and treat a non-empty
`path` only as a consistency check; otherwise cold resume keeps `history
> path > threadId` precedence.
- Add protocol, resume, and fork regression coverage for empty path
payloads; refresh app-server schema fixtures for the clarified params
docs.

## Tests
- `just fmt`
- `just write-app-server-schema`
- `cargo test -p codex-app-server-protocol
thread_path_params_deserialize_empty_path_as_none`
- `cargo test -p codex-app-server-protocol --test schema_fixtures`
- `cargo test -p codex-app-server empty_path`
- `RUST_MIN_STACK=8388608 cargo test -p codex-app-server --test all
thread_resume_rejects_mismatched_path_for_running_thread_id`
- `RUST_MIN_STACK=8388608 cargo test -p codex-app-server --test all
thread_resume_uses_path_over_non_running_thread_id`

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.schemas.json

@@ -15370,7 +15370,7 @@
       },
       "ThreadForkParams": {
         "$schema": "http://json-schema.org/draft-07/schema#",
-        "description": "There are two ways to fork a thread: 1. By thread_id: load the thread from disk by thread_id and fork it into a new thread. 2. By path: load the thread from disk by path and fork it into a new thread.\n\nIf using path, the thread_id param will be ignored.\n\nPrefer using thread_id whenever possible.",
+        "description": "There are two ways to fork a thread: 1. By thread_id: load the thread from disk by thread_id and fork it into a new thread. 2. By path: load the thread from disk by path and fork it into a new thread.\n\nIf using a non-empty path, the thread_id param will be ignored. Empty string path values are treated as absent.\n\nPrefer using thread_id whenever possible.",
         "properties": {
           "approvalPolicy": {
             "anyOf": [
@@ -16868,7 +16868,7 @@
       },
       "ThreadResumeParams": {
         "$schema": "http://json-schema.org/draft-07/schema#",
-        "description": "There are three ways to resume a thread: 1. By thread_id: load the thread from disk by thread_id and resume it. 2. By history: instantiate the thread from memory and resume it. 3. By path: load the thread from disk by path and resume it.\n\nThe precedence is: history > path > thread_id. If using history or path, the thread_id param will be ignored.\n\nPrefer using thread_id whenever possible.",
+        "description": "There are three ways to resume a thread: 1. By thread_id: load the thread from disk by thread_id and resume it. 2. By history: instantiate the thread from memory and resume it. 3. By path: load the thread from disk by path and resume it.\n\nFor non-running threads, the precedence is: history > non-empty path > thread_id. If using history or a non-empty path for a non-running thread, the thread_id param will be ignored.\n\nIf thread_id identifies a running thread, app-server rejoins that thread and treats a non-empty path as a consistency check against the active rollout path. Empty string path values are treated as absent.\n\nPrefer using thread_id whenever possible.",
         "properties": {
           "approvalPolicy": {
             "anyOf": [