### 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.
pnhb->add_child(create_dir);
	create_dir->set_text(TTR("Create Folder"));
	create_dir->connect("pressed", callable_mp(this, &ProjectDialog::_create_folder));
	path_container = memnew(VBoxContainer);
	vb->add_child(path_container);
	l = memnew(Label);
	l->set_text(TTR("Project Path:"));
	path_container->add_child(l);
	HBoxContainer *pphb = memnew(HBoxContainer);
	path_container->add_child(pphb);
	project_path = memnew(LineEd);
	project_path->set_h_size_flags(Control::SIZE_EXPAND_FILL);
	project_path->set_structured_text_bidi_override(TextServer::STRUCTURED_TEXT_FILE);
	pphb->add_child(project_path);
	install_path_container = memnew(VBoxContainer);
	vb->add_child(install_path_container);
	l = memnew(Label);
	l->set_text(TTR("Project Installation Path:"));
	install_path_container->add_child(l);
	HBoxContainer *iphb = memnew(HBoxContainer);
	install_path_container->add_child(iphb);
	install_path = memnew(LineEd);
	install_path->set_h_size_flags(Control::SIZE_EXPAND_FILL);
	install_path->set_structured_text_bidi_override(TextServer::STRUCTURED_TEXT_FILE);
	iphb->add_child(install_path);
	// status icon
	status_rect = Rect);
	status_rect->set_stretch_mode(TextureRect::STRETCH_KEEP_CENTERED);
	pphb->add_child(status_rect);
	browse = memnew(Button);