The same workflow works from the web UI but does not work from the API

### Custom Node Testing

- [x] I have tried disabling custom nodes and the issue persists (see [how to disable custom nodes](https://docs.comfy.org/troubleshooting/custom-node-issues#step-1%3A-test-with-all-custom-nodes-disabled) if you need help)

### Expected Behavior

The workflow should work properly from both web ui and api.

### Actual Behavior

The workflow works from web ui, but doesn't work from api.

### Steps to Reproduce

* create a workflow using web ui
* export it as an api
* send the workflow using api

[detect_box_and_save_image.json](https://github.com/user-attachments/files/22059237/detect_box_and_save_image.json)

### Debug Logs

```powershell
[2025-08-31 00:23:24.817] --- Logging error ---
[2025-08-31 00:23:24.817] got prompt
[2025-08-31 00:23:24.818] --- Logging error ---
[2025-08-31 00:23:24.818] invalid prompt: {'type': 'invalid_prompt', 'message': 'Cannot execute because node aichemyYOLOv8Segmentation does not exist.', 'details': "Node ID '#105'", 'extra_info': {}}
```

### Other

I have created a workflow using webui, and exported it as an api after confirming it works properly. and then I sent that workflow to comfyui server via /propmt API. I expected it works properly, but I got a "node does not exist error".
It's really storange because the custom node has been installed and I confirmed that workflow works properly before expoting it.
Just in case, I opened that api file from comfyui web ui and it was loaded and executed properly. I got the error whey only using API.

This workflow uses custom nodes, but since it works from the web UI and not from the API, I created this issue.
Is there any difference between running the same workflow from the web UI and running it via the /prompt API?

When I disabled custom nodes, this error no longer appears, but instead I get an error saying that the node is not installed (which is expected).