[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

```

まずローカルの POST /api/repos/{repositoryId}/worktrees フローを再現し、デスクトップアプリが認証済みの状態で、次にローカル websocket 経由で agent.prompt を送信します。手動で作成した workspace と API で作成した workspace の認証と初期化を比較します。API で作成した workspace が /login や retry のタイミングに関する問題なしに、初期 prompt を確実に受け付ければ完了です。

索引モデルが issue の本文から書いたものです。