### 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)

Vector<uint8_t> png_buffer;
	Error err = PNGDriverCommon::image_to_png(p_splash_image, png_buffer);
	if (err == OK) {
		p_data.resize(png_buffer.size());
		memcpy(p_data.ptrw(), png_buffer.ptr(), p_data.size());
	} else {
		String err_str = String("Failed to convert splash image to png.");
		WARN_PRINT(err_str.utf8().get_data());
	}
}
void EditorExportPlatformAndroid::_process_launcher_icons(const String &p_file_name, const Ref<Image> &p_source_image, int dimension, Vector<uint8_t> &p_data) {
	Ref<Image> working_image = p_source_image;
	if (p_source_image->get_width() != dimension || p_source_image->get_height() != dimension) {
		working_image = p_source_image->duplicate();
		working_image->resize(dimension, dimension, Image::Interpolation::INTERPOLATE_LANCZOS);
	}
	Vector<uint8_t> png_buffer;
	Error err = PNGDriverCommon::image_to_png(working_image, png_buffer);
	if (err == OK) {
		p_data.resize(png_buffer.size());
		memcpy(p_data.ptrw(), png_buffer.ptr(), p_data.size());
	} else {
		String err_str = String("Failed to convert resized icon (") + p_file_name + ") to png.";
		WARN_PRINT(err_str.utf8().get_data());
	}
}
String EditorExportPlatformAndroid::load_splash_refs(Ref<Image> &splash_image, Ref<Image> &splash_bg_color_image) {