### 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)

add_preset->get_popup()->clear();
	for (int i = 0; i < EditorExport::get_singleton()->get_export_platform_count(); i++) {
		Ref<EditorExportPlatform> plat = EditorExport::get_singleton()->get_export_platform(i);
		add_preset->get_popup()->add_icon_item(plat->get_logo(), plat->get_name());
	}
	_update_presets();
	if (presets->get_current() >= 0) {
		_update_current_preset(); 
	}
	
	Rect2 saved_size = EditorSettings::get_singleton()->get_project_metadata("dialog_bounds", "export", Rect2());
	if (saved_size != Rect2()) {
		popup(saved_size);
	} else {
		popup_centered_clamped(Size2(900, 700) * EDSCALE, 0.8);
	}
}
void ProjectExportDialog::_add_preset(int p_platform) {
	Ref<EditorExportPreset> preset = EditorExport::get_singleton()->get_export_platform(p_platform)->create_preset();
	ERR_FAIL_COND(!preset.is_valid());
	String preset_name = EditorExport::get_singleton()->get_export_platform(p_platform)->get_name();
	bool make_runnable = true;
	int attempt = 1;
	while (true) {
		bool valid = true;