### 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.
path_hb->add_child(explore_button);
		explore_button->connect("pressed", callable_mp(this, &ProjectListItemControl::_explore_button_pressed));
		project_path = memnew(Label);
		project_path->set_name("ProjectPath");
		project_path->set_structured_text_bidi_override(TextServer::STRUCTURED_TEXT_FILE);
		project_path->set_clip_text(true);
		project_path->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		project_path->set_modulate(Color(1, 1, 1, 0.5));
		path_hb->add_child(project_path);
		project_unsupported_features = Rect);
		project_unsupported_features->set_name("ProjectUnsupportedFeatures");
		project_unsupported_features->set_stretch_mode(TextureRect::STRETCH_KEEP_CENTERED);
		path_hb->add_child(project_unsupported_features);
		project_unsupported_features->hide();
		Control *spacer = memnew(Control);
		spacer->set_custom_minimum_size(Size2(10, 10));
		path_hb->add_child(spacer);
	}
}
struct ProjectListComparator {
	ProjectList::FilterOption order_option = ProjectList::FilterOption::EDIT_DATE;
	// operator<
	_FORCE_INLINE_ boo(const ProjectList::Item &a, const ProjectList::Item &b) const {
		if (a.favore && !b.favore) {
			return true;
		}
		if (b.favore && !a.favore) {
			return false;
		}
		swch (order_option) {