### 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)

if (p_preset->get("codesign/description") != "") {
#ifdef WINDOWS_ENABLED
		args.push_back("/d");
#else
		args.push_back("-n");
#endif
		args.push_back(p_preset->get("codesign/description"));
	}
	
	PackedStringArray user_args = p_preset->get("codesign/custom_options");
	for (int i = 0; i < user_args.size(); i++) {
		String user_arg = user_args[i].strip_edges();
		if (!user_arg.is_empty()) {
			args.push_back(user_arg);
		}
	}
#ifndef WINDOWS_ENABLED
	args.push_back("-in");
#endif
	args.push_back(p_path);
#ifndef WINDOWS_ENABLED
	args.push_back("-out");
	args.push_back(p_path + "_signed");
#endif
	String str;
	Error err = OS::get_singleton()->execute(signtool_path, args, &str, nullptr, true);
	if (err != OK || (str.find("not found") != -1) || (str.find("not recognized") != -1)) {
#ifdef WINDOWS_ENABLED
		add_message(EXPORT_MESSAGE_WARNING, TTR("Code Signing"), TTR("Could not start signtool executable. Configure signtool path in the Editor Settings (Export > Windows > signtool), or disable \"Codesign\" in the export preset."));