### 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)

unzGetCurrentFileInfo(pkg, &info, fname, 16384, nullptr, 0, nullptr, 0);
		String file = String::utf8(fname);
		
		if (file.ends_with("/")) {
			continue;
		}
		
		if (!pwa && (file == "godot.service.worker.js" || file == "godot.offline.html")) {
			continue;
		}
		Vector<uint8_t> data;
		data.resize(info.uncompressed_size);
		
		unzOpenCurrentFile(pkg);
		unzReadCurrentFile(pkg, data.ptrw(), data.size());
		unzCloseCurrentFile(pkg);
		
		String dst = p_dir.path_join(file.replace("godot", p_name));
		Ref<FileAccess> f = FileAccess::open(dst, FileAccess::WRITE);
		if (f.is_null()) {
			add_message(EXPORT_MESSAGE_ERROR, TTR("Prepare Templates"), vformat(TTR("Could not write file: \"%s\"."), dst));
			unzClose(pkg);
			return ERR_FILE_CANT_WRITE;
		}
		f->store_buffer(data.ptr(), data.size());
	} while (unzGoToNextFile(pkg) == UNZ_OK);
	unzClose(pkg);
	return OK;
}
Error EditorExportPlatformWeb::_write_or_error(const uint8_t *p_content, int p_size, String p_path) {