### 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)

Ref<DirAccess> da_res = DirAccess::create(DirAccess::ACCESS_RESOURCES);
	
	if (da_res->dir_exists(APK_ASSETS_DIRECTORY)) {
		print_verbose("Clearing APK assets directory...");
		Ref<DirAccess> da_assets = DirAccess::open(APK_ASSETS_DIRECTORY);
		ERR_FAIL_COND(da_assets.is_null());
		da_assets->erase_contents_recursive();
		da_res->remove(APK_ASSETS_DIRECTORY);
	}
	
	if (da_res->dir_exists(AAB_ASSETS_DIRECTORY)) {
		print_verbose("Clearing AAB assets directory...");
		Ref<DirAccess> da_assets = DirAccess::open(AAB_ASSETS_DIRECTORY);
		ERR_FAIL_COND(da_assets.is_null());
		da_assets->erase_contents_recursive();
		da_res->remove(AAB_ASSETS_DIRECTORY);
	}
}
void EditorExportPlatformAndroid::_remove_copied_libs() {