app-server: preserve target-native environment cwd (#28146)

## Why

app-server may run on a different OS from the selected exec-server
environment. Parsing that environment’s cwd with the Codex host’s path
rules prevents thread startup.

## What

Carry environment cwd values as `LegacyAppPathString` at the app-server
boundary and `PathUri` internally. Existing tool-call schemas and
relative-path behavior stay host-native; remaining local-only consumers
convert explicitly and leave follow-up TODOs.

The Wine integration test verifies app-server can start a thread and
complete an ordinary turn with a Windows environment cwd from Linux.

## Validation

- `bazel test //codex-rs/core/tests/remote_env_windows:smoke-test
--test_output=errors`
- focused app-server environment-selection and protocol schema tests
- scoped Clippy for `codex-core` and `codex-app-server-protocol`

codex-rs/app-server-protocol/schema/json/ClientRequest.json

@@ -1303,6 +1303,9 @@
       ],
       "type": "object"
     },
+    "LegacyAppPathString": {
+      "type": "string"
+    },
     "ListMcpServerStatusParams": {
       "properties": {
         "cursor": {
@@ -4331,7 +4334,7 @@
     "TurnEnvironmentParams": {
       "properties": {
         "cwd": {
-          "$ref": "#/definitions/AbsolutePathBuf"
+          "$ref": "#/definitions/LegacyAppPathString"
         },
         "environmentId": {
           "type": "string"

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

@@ -19517,7 +19517,7 @@
       "TurnEnvironmentParams": {
         "properties": {
           "cwd": {
-            "$ref": "#/definitions/v2/AbsolutePathBuf"
+            "$ref": "#/definitions/v2/LegacyAppPathString"
           },
           "environmentId": {
             "type": "string"

codex-rs/app-server-protocol/schema/json/codex_app_server_protocol.v2.schemas.json

@@ -17325,7 +17325,7 @@
     "TurnEnvironmentParams": {
       "properties": {
         "cwd": {
-          "$ref": "#/definitions/AbsolutePathBuf"
+          "$ref": "#/definitions/LegacyAppPathString"
         },
         "environmentId": {
           "type": "string"

codex-rs/app-server-protocol/schema/json/v2/ThreadStartParams.json

@@ -191,6 +191,9 @@
         }
       ]
     },
+    "LegacyAppPathString": {
+      "type": "string"
+    },
     "Personality": {
       "enum": [
         "none",
@@ -242,7 +245,7 @@
     "TurnEnvironmentParams": {
       "properties": {
         "cwd": {
-          "$ref": "#/definitions/AbsolutePathBuf"
+          "$ref": "#/definitions/LegacyAppPathString"
         },
         "environmentId": {
           "type": "string"

codex-rs/app-server-protocol/schema/json/v2/TurnStartParams.json

@@ -130,6 +130,9 @@
       ],
       "type": "string"
     },
+    "LegacyAppPathString": {
+      "type": "string"
+    },
     "ModeKind": {
       "description": "Initial collaboration mode to use when the TUI starts.",
       "enum": [
@@ -331,7 +334,7 @@
     "TurnEnvironmentParams": {
       "properties": {
         "cwd": {
-          "$ref": "#/definitions/AbsolutePathBuf"
+          "$ref": "#/definitions/LegacyAppPathString"
         },
         "environmentId": {
           "type": "string"

codex-rs/app-server-protocol/schema/typescript/v2/TurnEnvironmentParams.ts

@@ -1,6 +1,6 @@
 // GENERATED CODE! DO NOT MODIFY BY HAND!
 
 // This file was generated by [ts-rs](https://github.com/Aleph-Alpha/ts-rs). Do not edit this file manually.
-import type { AbsolutePathBuf } from "../AbsolutePathBuf";
+import type { LegacyAppPathString } from "../LegacyAppPathString";
 
-export type TurnEnvironmentParams = { environmentId: string, cwd: AbsolutePathBuf, };
+export type TurnEnvironmentParams = { environmentId: string, cwd: LegacyAppPathString, };