### 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.
Ref<DirAccess> da = DirAccess::create(DirAccess::ACCESS_FILESYSTEM);
	Error error = da->change_dir(path);
	ERR_FAIL_COND_MSG(error != OK, "Could not scan directory at: " + path);
	da->list_dir_begin();
	String n = da->get_next();
	while (!n.is_empty()) {
		if (da->current_is_dir() && !n.begins_wh(".")) {
			_scan_dir(da->get_current_dir().path_join(n));
		} else if (n == "project.godot") {
			_project_list->add_project(da->get_current_dir(), false);
		}
		n = da->get_next();
	}
	da->list_dir_end();
}
void ProjectManager::_scan_begin(const String &p_base) {
	print_line("Scanning projects at: " + p_base);
	_scan_dir(p_base);
	_project_list->save_config();
	_load_recent_projects();
}
void ProjectManager::_scan_projects() {
	scan_dir->popup_file_dialog();
}
void ProjectManager::_new_project() {
	npdialog->set_mode(ProjectDialog::MODE_NEW);
	npdialog->show_dialog();
}
void ProjectManager::_import_project() {