app-server: expose thread permission profiles (#18278)

## Why

The `PermissionProfile` migration needs app-server clients to see the
same constrained permission model that core is using at runtime. Before
this PR, thread lifecycle responses only exposed the legacy
`SandboxPolicy` shape, so clients still had to infer active permissions
from sandbox fields. That makes downstream resume, fork, and override
flows harder to make `PermissionProfile`-first.

External sandbox policies are intentionally excluded from this canonical
view. External enforcement cannot be round-tripped as a
`PermissionProfile`, and exposing a lossy root-write profile would let
clients accidentally change sandbox semantics if they echo the profile
back later.

## What changed

- Adds the app-server v2 `PermissionProfile` wire shape, including
filesystem permissions and glob scan depth metadata.
- Adds `PermissionProfileNetworkPermissions` so the profile response
does not expose active network state through the older
additional-permissions naming.
- Returns `permissionProfile` from thread start, resume, and fork
responses when the active sandbox can be represented as a
`PermissionProfile`.
- Keeps legacy `sandbox` in those responses for compatibility and
documents `permissionProfile` as canonical when present.
- Makes lifecycle `permissionProfile` nullable and returns `null` for
`ExternalSandbox` to avoid exposing a lossy profile.
- Regenerates the app-server JSON schema and TypeScript fixtures.

## Verification

- `cargo test -p codex-app-server-protocol`
- `cargo test -p codex-app-server
thread_response_permission_profile_omits_external_sandbox --
--nocapture`
- `cargo check --tests -p codex-analytics -p codex-exec -p codex-tui`
- `just fix -p codex-app-server-protocol -p codex-app-server -p
codex-analytics -p codex-exec -p codex-tui`

---
[//]: # (BEGIN SAPLING FOOTER)
Stack created with [Sapling](https://sapling-scm.com). Best reviewed
with [ReviewStack](https://reviewstack.dev/openai/codex/pull/18278).
* #18279
* __->__ #18278

codex-rs/app-server-protocol/src/protocol/common.rs

@@ -1435,6 +1435,7 @@ mod tests {
 
     #[test]
     fn serialize_client_response() -> Result<()> {
+        let cwd = absolute_path("/tmp");
         let response = ClientResponse::ThreadStart {
             request_id: RequestId::Integer(7),
             response: v2::ThreadStartResponse {
@@ -1448,7 +1449,7 @@ mod tests {
                     updated_at: 2,
                     status: v2::ThreadStatus::Idle,
                     path: None,
-                    cwd: absolute_path("/tmp"),
+                    cwd: cwd.clone(),
                     cli_version: "0.0.0".to_string(),
                     source: v2::SessionSource::Exec,
                     agent_nickname: None,
@@ -1460,11 +1461,18 @@ mod tests {
                 model: "gpt-5".to_string(),
                 model_provider: "openai".to_string(),
                 service_tier: None,
-                cwd: absolute_path("/tmp"),
+                cwd: cwd.clone(),
                 instruction_sources: vec![absolute_path("/tmp/AGENTS.md")],
                 approval_policy: v2::AskForApproval::OnFailure,
                 approvals_reviewer: v2::ApprovalsReviewer::User,
                 sandbox: v2::SandboxPolicy::DangerFullAccess,
+                permission_profile: Some(
+                    codex_protocol::models::PermissionProfile::from_legacy_sandbox_policy(
+                        &codex_protocol::protocol::SandboxPolicy::DangerFullAccess,
+                        cwd.as_path(),
+                    )
+                    .into(),
+                ),
                 reasoning_effort: None,
             },
         };
@@ -1507,6 +1515,24 @@ mod tests {
                     "sandbox": {
                         "type": "dangerFullAccess"
                     },
+                    "permissionProfile": {
+                        "network": {
+                            "enabled": true,
+                        },
+                        "fileSystem": {
+                            "entries": [
+                                {
+                                    "path": {
+                                        "type": "special",
+                                        "value": {
+                                            "kind": "root",
+                                        },
+                                    },
+                                    "access": "write",
+                                },
+                            ],
+                        },
+                    },
                     "reasoningEffort": null
                 }
             }),