app-server: use profile ids in v2 permission params (#23360)

## Why

The v2 app-server permission profile fields are experimental, but the
previous migration kept a legacy object payload for profile selection.
That made clients aware of server-owned `activePermissionProfile`
metadata such as `extends`, and it kept a
`legacy_additional_writable_roots` path even though
`runtimeWorkspaceRoots` now owns runtime workspace-root selection.

This PR makes the client contract match the intended model: clients
select a permission profile by id, and the server resolves and reports
active profile provenance in response payloads.

Follow-up to #22611.

## What Changed

- Changed `thread/start`, `thread/resume`, `thread/fork`, and
`turn/start` permission profile selection to plain profile id strings.
- Changed `command/exec.permissionProfile` to a plain profile id string
for the same client/server ownership split.
- Removed `PermissionProfileSelectionParams` and the legacy `{ type:
"profile", modifications: [...] }` compatibility deserializer.
- Updated app-server, TUI, and `codex exec` call sites to send only ids,
while keeping `activePermissionProfile` as server response metadata.
- Updated app-server docs and schema fixtures for the revised
`command/exec.permissionProfile` shape.

## Verification

- `cargo test -p codex-app-server-protocol`
- `RUST_MIN_STACK=8388608 cargo test -p codex-app-server`
- `cargo test -p codex-exec`
- `RUST_MIN_STACK=8388608 cargo test -p codex-tui`

---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/23360).
* #23368
* __->__ #23360

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

@@ -5,26 +5,6 @@
       "description": "A path that is guaranteed to be absolute and normalized (though it is not guaranteed to be canonicalized or exist on the filesystem).\n\nIMPORTANT: When deserializing an `AbsolutePathBuf`, a base path must be set using [AbsolutePathBufGuard::new]. If no base path is set, the deserialization will fail unless the path being deserialized is already absolute.",
       "type": "string"
     },
-    "ActivePermissionProfile": {
-      "properties": {
-        "extends": {
-          "default": null,
-          "description": "Parent profile identifier once permissions profiles support inheritance. This is currently always `null`.",
-          "type": [
-            "string",
-            "null"
-          ]
-        },
-        "id": {
-          "description": "Identifier from `default_permissions` or the implicit built-in default, such as `:workspace` or a user-defined `[permissions.<id>]` profile.",
-          "type": "string"
-        }
-      },
-      "required": [
-        "id"
-      ],
-      "type": "object"
-    },
     "AddCreditsNudgeCreditType": {
       "enum": [
         "credits",

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

@@ -5,26 +5,6 @@
       "description": "A path that is guaranteed to be absolute and normalized (though it is not guaranteed to be canonicalized or exist on the filesystem).\n\nIMPORTANT: When deserializing an `AbsolutePathBuf`, a base path must be set using [AbsolutePathBufGuard::new]. If no base path is set, the deserialization will fail unless the path being deserialized is already absolute.",
       "type": "string"
     },
-    "ActivePermissionProfile": {
-      "properties": {
-        "extends": {
-          "default": null,
-          "description": "Parent profile identifier once permissions profiles support inheritance. This is currently always `null`.",
-          "type": [
-            "string",
-            "null"
-          ]
-        },
-        "id": {
-          "description": "Identifier from `default_permissions` or the implicit built-in default, such as `:workspace` or a user-defined `[permissions.<id>]` profile.",
-          "type": "string"
-        }
-      },
-      "required": [
-        "id"
-      ],
-      "type": "object"
-    },
     "CommandExecTerminalSize": {
       "description": "PTY size in character cells for `command/exec` PTY sessions.",
       "properties": {