### 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)

store_image(launcher_icon.export_path, data);
}
void EditorExportPlatformAndroid::store_image(const String &export_path, const Vector<uint8_t> &data) {
	String img_path = export_path.insert(0, "res://android/build/");
	store_file_at_path(img_path, data);
}
void EditorExportPlatformAndroid::_copy_icons_to_gradle_project(const Ref<EditorExportPreset> &p_preset,
		const String &processed_splash_config_xml,
		const Ref<Image> &splash_image,
		const Ref<Image> &splash_bg_color_image,
		const Ref<Image> &main_image,
		const Ref<Image> &foreground,
		const Ref<Image> &background) {
	
	if (!processed_splash_config_xml.is_empty()) {
		print_verbose("Storing processed splash configuration: " + String("\n") + processed_splash_config_xml);
		store_string_at_path(SPLASH_CONFIG_PATH, processed_splash_config_xml);
	}
	
	if (splash_image.is_valid() && !splash_image->is_empty()) {
		print_verbose("Storing splash image in " + String(SPLASH_IMAGE_EXPORT_PATH));
		Vector<uint8_t> data;
		_load_image_data(splash_image, data);
		store_image(SPLASH_IMAGE_EXPORT_PATH, data);
	}
	
	if (splash_bg_color_image.is_valid() && !splash_bg_color_image->is_empty()) {
		print_verbose("Storing splash background image in " + String(SPLASH_BG_COLOR_PATH));