### 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)

texture_format_error_label = memnew(Label);
	add_child(texture_format_error_label);
	
	fix_texture_format_button = memnew(LinkButton);
	fix_texture_format_button->set_v_size_flags(Control::SIZE_SHRINK_CENTER);
	fix_texture_format_button->set_text(TTR("Fix Import"));
	add_child(fix_texture_format_button);
	fix_texture_format_button->connect("pressed", callable_mp(this, &ProjectExportTextureFormatError::_on_fix_texture_format_pressed));
}
void ProjectExportDialog::_notification(int p_what) {
	switch (p_what) {
		case NOTIFICATION_VISIBILITY_CHANGED: {
			if (!is_visible()) {
				EditorSettings::get_singleton()->set_project_metadata("dialog_bounds", "export", Rect2(get_position(), get_size()));
			}
		} break;
		case NOTIFICATION_THEME_CHANGED: {
			duplicate_preset->set_icon(presets->get_editor_theme_icon(SNAME("Duplicate")));
			delete_preset->set_icon(presets->get_editor_theme_icon(SNAME("Remove")));
		} break;
		case NOTIFICATION_READY: {
			duplicate_preset->set_icon(presets->get_editor_theme_icon(SNAME("Duplicate")));
			delete_preset->set_icon(presets->get_editor_theme_icon(SNAME("Remove")));
			connect("confirmed", callable_mp(this, &ProjectExportDialog::_export_pck_zip));
			_update_export_all();
		} break;
	}
}
void ProjectExportDialog::popup_export() {