### 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.
PackedStringArray tags;
	for (int i = 0; i < project_tags->get_child_count(); i++) {
		ProjectTag *tag_control = Object::cast_to<ProjectTag>(project_tags->get_child(i));
		if (tag_control) {
			tags.append(tag_control->get_tag());
		}
	}
	ConfigFile cfg;
	const String project_godot = _project_list->get_selected_projects()[0].path.path_join("project.godot");
	Error err = cfg.load(project_godot);
	if (err != OK) {
		tag_ed_error->set_text(vformat(TTR("Couldn't load project at '%s' (error %d). It may be missing or corrupted."), project_godot, err));
		tag_ed_error->show();
		callable_mp((Window *)tag_manage_dialog, &Window::show).call_deferred(); // Make sure the dialog does not disappear.
		return;
	} else {
		tags.sort();
		cfg.set_value("application", "config/tags", tags);
		err = cfg.save(project_godot);
		if (err != OK) {
			tag_ed_error->set_text(vformat(TTR("Couldn't save project at '%s' (error %d)."), project_godot, err));
			tag_ed_error->show();
			callable_mp((Window *)tag_manage_dialog, &Window::show).call_deferred();
			return;
		}
	}
	_on_projects_updated();
}
void ProjectManager::_set_new_tag_name(const String p_name) {