### Godot version

4.0.2

### System information

Windows 10, GPU with no Vulkan support

### Issue description

My GPU doesn't support Vulkan. I run Godot 4 with "--rendering-driver opengl3" argument.

I have tried to open my Godot 3 project from Godot 4 Project Manager. It asked me whether I want my project to be converted. I pressed "full conversion". Very shortly it gave me a error that it can't run Vulkan app and that I should use "--rendering-driver opengl3", which I already run. After it closed Project Manager for me and I reopened it, I could find the project in the Project Manager list and then open it. There was no error. However the convertion was minimal, just enough to run it in Godot 4. I believe that it didn't run a full auto-convertion.
This always happens when I repeat these steps.

Next I have used command line and launched Godot 4 from it with "--convert-3to4" argument, doing it on second copy of the same Godot 3 project. (Had to increase limits for it to convert everything.) The process went smoothly and final project could be opened without error as well. However it had a more full conversion in comparison. This makes me believe that conversion process fails in Project Manager method by not respecting "--rendering-driver opengl3" argument in the process (I don't know how it actually looks as I can't run it).

P.S. I also run Godot 4 with "--single-window" argument, as it glitches out for me otherwise. I don't know if it has an impact on my experience, but worth mentioning.

Bonus:
I have a suspicion that this issue 
https://github.com/godotengine/godot/issues/74159
is related to this one and is actually a result of a failed conversion.

### Steps to reproduce

Get GPU with no Vulkan support and try to convert any Godot 3 project from Project Manager while running with "--rendering-driver opengl3".

### Minimal reproduction project

Any Godot 3 project, it just has to error on attempt.
List<String> args = OS::get_singleton()->get_cmdline_args();
	Error err = OS::get_singleton()->create_instance(args);
	ERR_FAIL_COND(err);
	_dim_window();
	get_tree()->qu();
}
void ProjectManager::_install_project(const String &p_zip_path, const String &p_tle) {
	npdialog->set_mode(ProjectDialog::MODE_INSTALL);
	npdialog->set_zip_path(p_zip_path);
	npdialog->set_zip_tle(p_tle);
	npdialog->show_dialog();
}
void ProjectManager::_files_dropped(PackedStringArray p_files) {
	if (p_files.size() == 1 && p_files[0].ends_wh(".zip")) {
		const String file = p_files[0].get_file();
		_install_project(p_files[0], file.substr(0, file.length() - 4).capalize());
		return;
	}
	HashSet<String> folders_set;
	Ref<DirAccess> da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
	for (int i = 0; i < p_files.size(); i++) {
		String file = p_files[i];
		folders_set.insert(da->dir_exists(file) ? file : file.get_base_dir());
	}
	if (folders_set.size() > 0) {
		PackedStringArray folders;