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/src/export.rs

@@ -2747,7 +2747,7 @@ export type Config = { stableField: Keep, unstableField: string | null } & ({ [k
         let _guard = TempDirGuard(output_dir.clone());
         let path = output_dir.join("CommandExecParams.ts");
         let content = r#"import type { CommandExecTerminalSize } from "./CommandExecTerminalSize";
-import type { PermissionProfile } from "./PermissionProfile";
+import type { ActivePermissionProfile } from "./ActivePermissionProfile";
 import type { SandboxPolicy } from "./SandboxPolicy";
 
 export type CommandExecParams = {/**
@@ -2770,12 +2770,12 @@ size?: CommandExecTerminalSize | null, /**
  */
 sandboxPolicy?: SandboxPolicy | null,
 /**
- * Optional full permissions profile for this command.
+ * Optional active permissions profile for this command.
  *
  * Defaults to the user's configured permissions when omitted. Cannot be
  * combined with `sandboxPolicy`.
  */
-permissionProfile?: PermissionProfile | null};
+permissionProfile?: ActivePermissionProfile | null};
 "#;
         fs::write(&path, content)?;
 
@@ -2789,11 +2789,13 @@ permissionProfile?: PermissionProfile | null};
 
         let filtered = fs::read_to_string(&path)?;
         assert_eq!(
-            filtered.contains("permissionProfile?: PermissionProfile"),
+            filtered.contains("permissionProfile?: ActivePermissionProfile"),
             false
         );
         assert_eq!(
-            filtered.contains(r#"import type { PermissionProfile } from "./PermissionProfile";"#),
+            filtered.contains(
+                r#"import type { ActivePermissionProfile } from "./ActivePermissionProfile";"#
+            ),
             false
         );
         assert_eq!(filtered.contains("sandboxPolicy?: SandboxPolicy"), true);