app-server-protocol: remove PermissionProfile from API (#22924)

## Why

The app server API should expose permission profile identity, not the
lower-level runtime permission model. `PermissionProfile` is the
compiled sandbox/network representation that the server uses internally;
exposing it through app-server-protocol forces clients to understand
details that should remain implementation-level.

The API boundary should prefer `ActivePermissionProfile`: a stable
profile id, plus future parent-profile metadata, that clients can pass
back when they want to select the same active permissions. This also
avoids schema generation collisions between the app-server v2 API type
space and the core protocol model.

Incidentally, while PR makes a number of changes to `command/exec`, note
that we are hoping to deprecate this API in favor of `process/spawn`, so
we don't need to be too finicky about these changes.

## What Changed

- Removed `PermissionProfile` from the app-server-protocol API surface,
including generated schema and TypeScript exports.
- Changed `CommandExecParams.permissionProfile` to
`ActivePermissionProfile`.
- Resolve command exec profile ids through `ConfigManager` for the
command cwd, matching turn override selection semantics.
- Updated downstream TUI tests/helpers to use core permission types
directly instead of app-server-protocol `PermissionProfile` shims.

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

@@ -8168,135 +8168,6 @@
         }
       ]
     },
-    "PermissionProfile": {
-      "oneOf": [
-        {
-          "description": "Codex owns sandbox construction for this profile.",
-          "properties": {
-            "fileSystem": {
-              "$ref": "#/definitions/PermissionProfileFileSystemPermissions"
-            },
-            "network": {
-              "$ref": "#/definitions/PermissionProfileNetworkPermissions"
-            },
-            "type": {
-              "enum": [
-                "managed"
-              ],
-              "title": "ManagedPermissionProfileType",
-              "type": "string"
-            }
-          },
-          "required": [
-            "fileSystem",
-            "network",
-            "type"
-          ],
-          "title": "ManagedPermissionProfile",
-          "type": "object"
-        },
-        {
-          "description": "Do not apply an outer sandbox.",
-          "properties": {
-            "type": {
-              "enum": [
-                "disabled"
-              ],
-              "title": "DisabledPermissionProfileType",
-              "type": "string"
-            }
-          },
-          "required": [
-            "type"
-          ],
-          "title": "DisabledPermissionProfile",
-          "type": "object"
-        },
-        {
-          "description": "Filesystem isolation is enforced by an external caller.",
-          "properties": {
-            "network": {
-              "$ref": "#/definitions/PermissionProfileNetworkPermissions"
-            },
-            "type": {
-              "enum": [
-                "external"
-              ],
-              "title": "ExternalPermissionProfileType",
-              "type": "string"
-            }
-          },
-          "required": [
-            "network",
-            "type"
-          ],
-          "title": "ExternalPermissionProfile",
-          "type": "object"
-        }
-      ]
-    },
-    "PermissionProfileFileSystemPermissions": {
-      "oneOf": [
-        {
-          "properties": {
-            "entries": {
-              "items": {
-                "$ref": "#/definitions/FileSystemSandboxEntry"
-              },
-              "type": "array"
-            },
-            "globScanMaxDepth": {
-              "format": "uint",
-              "minimum": 1.0,
-              "type": [
-                "integer",
-                "null"
-              ]
-            },
-            "type": {
-              "enum": [
-                "restricted"
-              ],
-              "title": "RestrictedPermissionProfileFileSystemPermissionsType",
-              "type": "string"
-            }
-          },
-          "required": [
-            "entries",
-            "type"
-          ],
-          "title": "RestrictedPermissionProfileFileSystemPermissions",
-          "type": "object"
-        },
-        {
-          "properties": {
-            "type": {
-              "enum": [
-                "unrestricted"
-              ],
-              "title": "UnrestrictedPermissionProfileFileSystemPermissionsType",
-              "type": "string"
-            }
-          },
-          "required": [
-            "type"
-          ],
-          "title": "UnrestrictedPermissionProfileFileSystemPermissions",
-          "type": "object"
-        }
-      ]
-    },
-    "PermissionProfileNetworkPermissions": {
-      "properties": {
-        "enabled": {
-          "type": "boolean"
-        }
-      },
-      "required": [
-        "enabled"
-      ],
-      "type": "object"
-    },
     "Personality": {
       "enum": [
         "none",