### 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)

cleanup();
	if (p_device) { 
		return OK;
	}
	EditorProgress ep("run", TTR("Running..."), 5);
	const String dest = EditorPaths::get_singleton()->get_cache_dir().path_join("linuxbsd");
	Ref<DirAccess> da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
	if (!da->dir_exists(dest)) {
		Error err = da->make_dir_recursive(dest);
		if (err != OK) {
			EditorNode::get_singleton()->show_warning(TTR("Could not create temp directory:") + "\n" + dest);
			return err;
		}
	}
	String host = p_preset->get("ssh_remote_deploy/host").operator String();
	String port = p_preset->get("ssh_remote_deploy/port").operator String();
	if (port.is_empty()) {
		port = "22";
	}
	Vector<String> extra_args_ssh = p_preset->get("ssh_remote_deploy/extra_args_ssh").operator String().split(" ", false);
	Vector<String> extra_args_scp = p_preset->get("ssh_remote_deploy/extra_args_scp").operator String().split(" ", false);
	const String basepath = dest.path_join("tmp_linuxbsd_export");
#define CLEANUP_AND_RETURN(m_err)                      \