### 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.
add_child(dialog_error);
		if (asset_library) {
			open_templates = memnew(ConfirmationDialog);
			open_templates->set_text(TTR("You currently don't have any projects.\nWould you like to explore official example projects in the Asset Library?"));
			open_templates->set_ok_button_text(TTR("Open Asset Library"));
			open_templates->connect("confirmed", callable_mp(this, &ProjectManager::_open_asset_library));
			add_child(open_templates);
		}
		about = memnew(EdorAbout);
		add_child(about);
		_build_icon_type_cache(get_theme());
	}
	{
		// Tag management.
		tag_manage_nfirmationDialog);
		add_child(tag_manage_dialog);
		tag_manage_dialog->set_tle(TTR("Manage Project Tags"));
		tag_manage_dialog->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_apply_project_tags));
		manage_tags_btn->connect("pressed", callable_mp(this, &ProjectManager::_manage_project_tags));
		VBoxContainer *tag_vb = memnew(VBoxContainer);
		tag_manage_dialog->add_child(tag_vb);
		Label *label = memnew(Label(TTR("Project Tags")));
		tag_vb->add_child(label);
		label->set_theme_type_variation("HeaderMedium");
		label->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_CENTER);
		label = memnew(Label(TTR("Click tag to remove  from the project.")));
		tag_vb->add_child(label);
		label->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_CENTER);
		project_tags = memnew(HFlowContainer);
		tag_vb->add_child(project_tags);