Loading API Format prompt workflow should handle missing nodes and still load graph (align behavior with loading of normal workflows)

### 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?

Expected:
Workflow should load even if specific custom node(s) are not installed, while displaying the appropriate dialogue about the missing custom node(s).

Actual:
The workflow does not load at all, although the correct dialogue for the missing custom node(s) is shown.

### Steps to Reproduce

1. Make sure not to have Comfy-Deploy (https://github.com/BennyKok/comfyui-deploy) and ComfyUI-Omini-Kontext (https://github.com/tercumantanumut/ComfyUI-Omini-Kontext) installed.
2. Attempt to drag and drop both/either of the workflows.
3. Notice the correct dialogue pop-up, but the workflow(s) not importing.

https://github.com/user-attachments/assets/3dde3364-11c0-439c-9f95-1fd3e1d2b451

[kontext-single-workflow.json](https://github.com/user-attachments/files/21975359/kontext-single-workflow.json)

[kontext-multi-workflow.json](https://github.com/user-attachments/files/21975360/kontext-multi-workflow.json)

### How is this affecting you?

Feature doesn't work as expected

### ComfyUI Frontend Version

1.26.6

### Browser

Chrome/Chromium

### Console Errors

```javascript

```

### Logs

```shell

```

### Additional Context

Workflows load correctly if the required custom node(s) are already installed before importing. However, if a workflow was previously loaded and the custom node(s) are uninstalled afterward, ComfyUI can still launch that workflow successfully on startup, since it reloads the last saved session.

┆Issue is synchronized with this [Notion page](https://www.notion.so/Issue-5198-community-workflows-do-not-import-if-contains-uninstalled-custom-nodes-25a6d73d36508192a476cc60bbf52574) by [Unito](https://www.unito.io)

Start by reproducing the drag-and-drop import with kontext-single-workflow.json or kontext-multi-workflow.json while the referenced custom nodes are absent, then trace the API Format prompt workflow loading path. Done means the missing-node dialog still appears and the workflow graph loads, matching normal workflow behavior.

Written by the indexing model from the issue text.