### 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.
browse->set_text(TTR("Browse"));
	browse->connect("pressed", callable_mp(this, &ProjectDialog::_browse_path));
	pphb->add_child(browse);
	// install status icon
	instal(TextureRect);
	install_status_rect->set_stretch_mode(TextureRect::STRETCH_KEEP_CENTERED);
	iphb->add_child(install_status_rect);
	install_browse = memnew(Button);
	install_browse->set_text(TTR("Browse"));
	install_browse->connect("pressed", callable_mp(this, &ProjectDialog::_browse_install_path));
	iphb->add_child(install_browse);
	msg = memnew(Label);
	msg->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_CENTER);
	vb->add_child(msg);
	// Renderer selection.
	renderVBoxContainer);
	vb->add_child(renderer_container);
	l = memnew(Label);
	l->set_text(TTR("Renderer:"));
	renderer_container->add_child(l);
	HBoxContainer *rshc = memnew(HBoxContainer);
	renderer_container->add_child(rshc);
	renderer_button_group.instantiate();
	// Left hand side, used for checkboxes to select renderer.
	Container *rvb = memnew(VBoxContainer);
	rshc->add_child(rvb);
	String default_renderer_type = "forward_plus";
	if (EdorSeteton()->has_setting("project_manager/default_renderer")) {
		default_renderer_type = EdorSeteton()->get_setting("project_manager/default_renderer");
	}