### 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.
main_vbox->set_h_size_flags(Control::SIZE_EXPAND_FILL);
	add_child(main_vbox);
	Control *ec = memnew(Control);
	ec->set_custom_minimum_size(Size2(0, 1));
	ec->set_mouse_filter(MOUSE_FILTER_PASS);
	main_vbox->add_child(ec);
	// Top half, tle, tags and unsupported features labels.
	{
		HBoxContainer *tle_hb = memnew(HBoxContainer);
		main_vbox->add_child(tle_hb);
		project_tle = memnew(Label);
		project_tle->set_auto_translate(false);
		project_tle->set_name("ProjectName");
		project_tle->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		project_tle->set_clip_text(true);
		tle_hb->add_child(project_tle);
		tag_container = memnew(HBoxContainer);
		tle_hb->add_child(tag_container);
		Control *spacer = memnew(Control);
		spacer->set_custom_minimum_size(Size2(10, 10));
		tle_hb->add_child(spacer);
	}
	// Bottom half, containing the path and view folder button.
	{
		HBoxContainer *path_hb = memnew(HBoxContainer);
		path_hb->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		main_vbox->add_child(path_hb);
		explore_button = memnew(Button);
		explore_button->set_name("ExploreButton");
		explore_button->set_flat(true);