### 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)

String clean_script = p_preset->get("ssh_remote_deploy/cleanup_script");
		clean_script = clean_script.replace("{temp_dir}", temp_dir);
		clean_script = clean_script.replace("{archive_name}", basepath.get_file() + ".zip");
		clean_script = clean_script.replace("{exe_name}", basepath.get_file());
		clean_script = clean_script.replace("{cmd_args}", cmd_args);
		Ref<FileAccess> f = FileAccess::open(basepath + "_clean.sh", FileAccess::WRITE);
		if (f.is_null()) {
			CLEANUP_AND_RETURN(err);
		}
		f->store_string(clean_script);
	}
	print_line("Uploading scripts...");
	ep.step(TTR("Uploading scripts..."), 4);
	err = ssh_push_to_remote(host, port, extra_args_scp, basepath + "_start.sh", temp_dir);
	if (err != OK) {
		CLEANUP_AND_RETURN(err);
	}
	err = ssh_run_on_remote(host, port, extra_args_ssh, vformat("chmod +x \"%s/%s\"", temp_dir, basepath.get_file() + "_start.sh"));
	if (err != OK || temp_dir.is_empty()) {
		CLEANUP_AND_RETURN(err);
	}
	err = ssh_push_to_remote(host, port, extra_args_scp, basepath + "_clean.sh", temp_dir);
	if (err != OK) {
		CLEANUP_AND_RETURN(err);
	}
	err = ssh_run_on_remote(host, port, extra_args_ssh, vformat("chmod +x \"%s/%s\"", temp_dir, basepath.get_file() + "_clean.sh"));
	if (err != OK || temp_dir.is_empty()) {
		CLEANUP_AND_RETURN(err);
	}
	print_line("Starting project...");