Nodes Execution Elow Do Not Display When Reconnecting to Local Instance via API

### Expected Behavior

The UI should display the execution flow, including updates and visual progress of node processing, even after reconnecting.

### Actual Behavior

When connected to a local ComfyUI instance via API, closing the GUI window and reopening it results in a loss of execution flow visualization. The nodes still process on the remote machine, but the execution flow (arrows, updates, or progress indicators, outputs, etc) does not update the UI until another prompt is submitted on that session.

### Steps to Reproduce

- Connect to a local ComfyUI instance via API.
- Submit a prompt and observe nodes generating.
- Close the GUI window (without stopping the local instance).
- Reopen the GUI and reconnect to the same instance.
- Submit another prompt.

### Debug Logs

```powershell
N/A
```

### Other

If someone just tells me what I'd need to do to reconnect to the WS instance I could most likely do a PR. I just don't want to learn a new codebase to fix this low of an issue.

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*This issue is transferred from: https://github.com/comfyanonymous/ComfyUI/issues/7033*

Original issue was created by @wes-kay at 2025-03-02T01:50:52.000Z

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-6430-Nodes-Execution-Elow-Do-Not-Display-When-Reconnecting-to-Local-Instance-via-API-29c6d73d3650812999aef32dfc8acb66) by [Unito](https://www.unito.io)