Propagate permission approval environment id (#25862)

## Stack

1. #25850 - Key request-permission grants by environment: stores and
applies sticky permission grants per environment id.
2. #25858 - Add `environmentId` to `request_permissions`: lets the model
target a selected environment and resolves relative permission paths
against it.
3. This PR (#25862) - Propagate permission approval environment id:
carries the selected environment id through approval events, app-server
requests, TUI prompts, and delegate forwarding.
4. #25867 - Add remote request permissions integration coverage:
verifies the selected remote environment across request, approval, grant
reuse, and exec.

This PR is stacked on #25858, and #25867 is stacked on this PR.

## Why

PR2 lets the model bind a `request_permissions` call to a selected
environment, but the approval event and client-facing request still
needed to carry that binding. For CCA, the user-facing prompt and
delegated approval path should know which environment the grant applies
to instead of relying on cwd alone.

## What Changed

- Added optional `environmentId` to `RequestPermissionsEvent`.
- Emit the selected environment id from core permission approval events.
- Preserve the environment id through delegate forwarding, including
cwd-based delegated requests.
- Added `environmentId` to app-server permission approval params,
generated schema/TypeScript artifacts, and README examples.
- Preserve and display the environment id in TUI permission approval
prompts.
- Updated focused core, app-server protocol, and TUI conversion
coverage.

## Testing

Not run locally per instruction. Performed read-only `git diff --check`.

codex-rs/tui/src/app/app_server_requests.rs

@@ -489,6 +489,7 @@ mod tests {
                     thread_id: "thread-1".to_string(),
                     turn_id: "turn-1".to_string(),
                     item_id: "perm-1".to_string(),
+                    environment_id: None,
                     started_at_ms: 0,
                     cwd: absolute_path(if cfg!(windows) { r"C:\tmp" } else { "/tmp" }),
                     reason: None,

codex-rs/tui/src/app/event_dispatch.rs

@@ -1856,12 +1856,20 @@ impl App {
                     ));
                 }
                 ApprovalRequest::Permissions {
+                    environment_id,
                     permissions,
                     reason,
                     ..
                 } => {
                     let _ = tui.enter_alt_screen();
                     let mut lines = Vec::new();
+                    if let Some(environment_id) = environment_id {
+                        lines.push(Line::from(vec![
+                            "Environment: ".into(),
+                            environment_id.bold(),
+                        ]));
+                        lines.push(Line::from(""));
+                    }
                     if let Some(reason) = reason {
                         lines.push(Line::from(vec!["Reason: ".into(), reason.italic()]));
                         lines.push(Line::from(""));

codex-rs/tui/src/app/tests.rs

@@ -2539,6 +2539,7 @@ async fn inactive_thread_permissions_approval_preserves_file_system_permissions(
             thread_id: thread_id.to_string(),
             turn_id: "turn-approval".to_string(),
             item_id: "call-approval".to_string(),
+            environment_id: Some("remote".to_string()),
             started_at_ms: 0,
             cwd: test_absolute_path("/tmp"),
             reason: Some("Need access to .git".to_string()),
@@ -2557,7 +2558,9 @@ async fn inactive_thread_permissions_approval_preserves_file_system_permissions(
     };
 
     let Some(ThreadInteractiveRequest::Approval(ApprovalRequest::Permissions {
-        permissions, ..
+        environment_id,
+        permissions,
+        ..
     })) = app
         .interactive_request_for_thread_request(thread_id, &request)
         .await
@@ -2565,6 +2568,7 @@ async fn inactive_thread_permissions_approval_preserves_file_system_permissions(
         panic!("expected permissions approval request");
     };
 
+    assert_eq!(environment_id.as_deref(), Some("remote"));
     assert_eq!(
         permissions,
         RequestPermissionProfile {

codex-rs/tui/src/app/thread_routing.rs

@@ -310,6 +310,7 @@ impl App {
                     thread_id,
                     thread_label,
                     call_id: params.item_id.clone(),
+                    environment_id: params.environment_id.clone(),
                     reason: params.reason.clone(),
                     permissions: params.permissions.clone().into(),
                 }),