### 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.
center_box->set_v_size_flags(Control::SIZE_EXPAND_FILL);
	vb->add_child(center_box);
	tabs = memnew(TabContainer);
	center_box->add_child(tabs);
	tabs->set_anchors_and_offsets_preset(Control::PRESET_FULL_RECT);
	tabs->connect("tab_changed", callable_mp(this, &ProjectManager::_on_tab_changed));
	local_projects_hb = memnew(HBoxContainer);
	local_projects_hb->set_name(TTR("Local Projects"));
	tabs->add_child(local_projects_hb);
	{
		// Projects + search bar
		VBoxC = memnew(VBoxContainer);
		local_projects_hb->add_child(search_tree_vb);
		search_tree_vb->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		HBoxContainer *hb = memnew(HBoxContainer);
		hb->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		search_tree_vb->add_child(hb);
		search_box = memnew(LineEd);
		search_box->set_placeholder(TTR("Filter Projects"));
		search_box->set_tooltip_text(TTR("This field filters projects by name and last path component.\nTo filter projects by name and full path, the query must contain at least one `/` character."));
		search_box->set_clear_button_enabled(true);
		search_box->connect("text_changed", callable_mp(this, &ProjectManager::_on_search_term_changed));
		search_box->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		hb->add_child(search_box);
		loading_label = memnew(Label(TTR("Loading, please wa...")));
		loading_label->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		hb->add_child(loading_label);
		// The loading label is shown later.
		loading_label->hide();
		Label *sort_label = memnew(Label);