### Tested versions

Godot Engine v4.2.stable.official.46dc27791

### System information

Windows 10

### Issue description

When exporting to web, Godot fails with this error in the console:

> scene/main/window.cpp:884 - Attempting to make child window exclusive, but the parent window already has another exclusive child. This window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->VBoxContainer@<!-- -->137/@<!-- -->AcceptDialog@<!-- -->411, parent window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559, current exclusive child window: /root/@<!-- -->EditorNode@<!-- -->17120/@<!-- -->Panel@<!-- -->13/@<!-- -->ProjectExportDialog@<!-- -->559/@<!-- -->ProgressDialog@<!-- -->17444

![a](https://github.com/godotengine/godot/assets/2000051/bf9d22aa-d3fe-4e11-bff6-c387e740fe90)

This happens for newly created empty projects.


### Steps to reproduce

1. Open the attached project (or create a new project).
2. Project->Export->Export All
3. Observe the console error.  No output files are generated.


### Minimal reproduction project (MRP)

[export_test.zip](https://github.com/godotengine/godot/files/13574810/export_test.zip)

ERR_FAIL_COND_V_MSG(p_total < 1, ERR_PARAMETER_RANGE_ERROR, "Must select at least one file to export.");
	String path = p_path.replace_first("res://", "");
	ZipData *zd = (ZipData *)p_userdata;
	zipFile zip = (zipFile)zd->zip;
	zipOpenNewFileInZip(zip,
			path.utf8().get_data(),
			nullptr,
			nullptr,
			0,
			nullptr,
			0,
			nullptr,
			Z_DEFLATED,
			Z_DEFAULT_COMPRESSION);
	zipWriteInFileInZip(zip, p_data.ptr(), p_data.size());
	zipCloseFileInZip(zip);
	if (zd->ep->step(TTR("Storing File:") + " " + p_path, 2 + p_file * 100 / p_total, false)) {
		return ERR_SKIP;
	}
	return OK;
}
Ref<ImageTexture> EditorExportPlatform::get_option_icon(int p_index) const {