“ERROR: EditorSettings not instantiated yet.” with `--dump-extension-api-with-docs`

### Tested versions

* Steam stable versions
* Reproducible in 4.4.0; did not encounter in earlier versions

### System information

Windows 11

### Issue description

```console
$ godot.lnk --dump-extension-api-with-docs
Dumping Extension API including documentation
Godot Engine v4.4.stable.steam.4c311cbee - https://godotengine.org
Vulkan 1.3.278 - Forward+ - Using Device #0: NVIDIA - NVIDIA GeForce RTX 2070 Super with Max-Q Design

ERROR: EditorSettings not instantiated yet.
at: (editor/editor_settings.cpp:1422)

# No error with no docs
$ godot.lnk --dump-extension-api
Dumping Extension API
Godot Engine v4.4.stable.steam.4c311cbee - https://godotengine.org
Vulkan 1.3.278 - Forward+ - Using Device #0: NVIDIA - NVIDIA GeForce RTX 2070 Super with Max-Q Design
```

### Steps to reproduce

```console
$ godot.lnk --dump-extension-api-with-docs
```

### Minimal reproduction project (MRP)

N/A

Start by running --dump-extension-api-with-docs on the reported Godot 4.4 environment and compare it with --dump-extension-api, which does not show the error. Trace the extension API documentation dump entry point and determine why EditorSettings is unavailable; done means the documented API dump completes without the error while still including documentation.

Written by the indexing model from the issue text.