Some subgraph inputs lose their edit boxes when saved as a blueprint

### Prerequisites

- [x] I am running the latest version of ComfyUI
- [x] I have searched existing issues to make sure this isn't a duplicate
- [x] I have tested with all custom nodes disabled ([see how](https://docs.comfy.org/troubleshooting/custom-node-issues#step-1%3A-test-with-all-custom-nodes-disabled))

### What happened?

When I save a subgraph as a blueprint some of the inputs lose their edit boxes:

The "Container" subgraph was saved as a blueprint. The "Blueprint" subgraph is the result added to the workflow from the Subgraph Blueprints entry in the Nodes menu.

They should look the same.

### Steps to Reproduce

1. Create a subgraph with some string nodes and connect these up to inputs:

2. Embed the subgraph into another subgraph and connect up some of its inputs:

3. The outer subgraph now looks like this:

4. Save the subgraph as a blueprint and _refresh the browser window_

5. From the Nodes menu, pick the Subgraph Blueprint you just created and drop it on the page

6. The resulting subgraph is deformed, with missing edit box:

7. Opening the subgraph you can see the embedded subgraph is similarly deformed:

### How is this affecting you?

Feature doesn't work as expected

### ComfyUI Frontend Version

1.32.1

### Browser

Chrome/Chromium

### Console Errors

```javascript

```

### Logs

```shell

```

### Additional Context

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-6587-Some-subgraph-inputs-lose-their-edit-boxes-when-saved-as-a-blueprint-2a26d73d365081218b4bd00e929239f4) by [Unito](https://www.unito.io)