[Bug]: API-created workspace initial prompt replies "Not logged in · Please run /login"

### Platform

macOS

### Operating system version

macOS 26.5.2 build 25F84

### System architecture

ARM64 (M1, M2, etc)

### PolyScope Version

0.26.0

### Bug description

When creating a workspace through the local Polyscope REST API and then sending the initial prompt over the local Polyscope websocket, the prompt sometimes fails with:

```text
Not logged in · Please run /login
```

The workspace itself is created successfully, but the initial agent prompt is rejected as unauthenticated.

This happens even though Polyscope is open and authenticated for normal/manual workspace usage.

## Request Flow

Workspace creation:

```http
POST http://127.0.0.1:4321/api/repos/{repositoryId}/worktrees
Accept: application/json
Content-Type: application/json
```

Payload:

```json
{
"branch": "dev/example-task",
"name": "dev/example-task"
}
```

The prompt is then sent over the local websocket:

```json
{
"type": "agent.prompt",
"worktreeId": "{worktreeId}",
"prompt": "{initial prompt text}"
}
```

Polyscope replies with:

```text
Not logged in · Please run /login
```

## Expected Behavior

If the Polyscope desktop app is already authenticated and manual prompting works, API-created workspaces should be able to receive the initial prompt without requiring `/login`.

## Actual Behavior

The workspace is created, but the initial prompt fails with:

```text
Not logged in · Please run /login
```

## Notes

I added retries on my side because this initially looked like a transient timing issue immediately after workspace creation. The error still surfaces enough that it seems like either:

- the API/websocket-created agent session is not inheriting the app's authenticated state, or
- Polyscope is accepting the prompt before the workspace agent/auth state is fully initialized.

This is separate from the cloud API. Workspace creation and prompting are both going through the local Polyscope desktop API/server.

### Steps to reproduce

_No response_

### Relevant log output

```shell

```

Bắt đầu bằng cách tái hiện flow cục bộ POST /api/repos/{repositoryId}/worktrees, sau đó gửi agent.prompt qua websocket cục bộ trong khi ứng dụng desktop đã được xác thực. So sánh việc xác thực và khởi tạo giữa các workspace được tạo thủ công và các workspace được tạo qua API. Được xem là hoàn tất khi một workspace được tạo qua API chấp nhận prompt ban đầu một cách ổn định mà không gặp vấn đề về /login hoặc thời điểm retry.

Do mô hình lập chỉ mục viết ra từ nội dung của issue.