Inconsistent renaming conventions and functions for widgets in subgraphs (nodes v1)

### 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?

Renaming conventions and functions seem to be inconsistent for widgets in subgraphs:

- Right-click, `Rename Widget: value` works outside of a subgraph, but not "remembered" inside.
- No apparent way to rename a widget value from the subgraphs panel, or at all unless the widget is connected as an input link in the subgraph

### Steps to Reproduce

1. Start a new workflow.
2. Add a node, such as string node.
3. Convert to subgraph.
4. Enter subgraph.
5. Connect `value` widget as input link in the subgraph.
6. Right-click on the node widget itself and rename to `node_value`.
7. The new name does not change the input link name, which is still `value`.
8. Add an additional string node.
9. Connect `value` widget as an additional input link in the subgraph.
10. Right-click and rename input link from `value_1` to `internal_value`.
11. Exit subgraph.
12. Right-click on the `value` widget and rename to `external_value`.
13. Enter subgraph.
14. Notice the input link still shows `value`.
15. So, renaming subgraph input links works from the inside-out, but not from the outside-in. (And also, in related testing, not when first renaming the widget before connecting it as an input link in a subgraph.)
16. Add a different kind of node, such as an integer node; do not connect anything.
17. Exit the subgraph.
18. Open the Edit Subgraphs Widgets panel.
19. Notice the listed widget names are the default/generic `value`, `value_1`, etc.
20. There is no function in the panel to rename the widgets.
21. Click to make visible the new integer node widget.
22. On the subgraph, right-click the integer widget.
23. There is no option to rename the widget.

### How is this affecting you?

Feature doesn't work as expected

### ComfyUI Frontend Version

1.34.9

### Browser

Chrome/Chromium

### Console Errors

```javascript

```

### Logs

```shell

```

### Additional Context

_No response_

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-7739-Inconsistent-renaming-conventions-and-functions-for-widgets-in-subgraphs-nodes-v1-2d26d73d3650814ab5a1ed67fd426d63) by [Unito](https://www.unito.io)