### 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.
sort_label->set_text(TTR("Sort:"));
		hb->add_child(sort_label);
		filter_option = memnew(OptionButton);
		filter_option->set_clip_text(true);
		filter_option->set_h_size_flags(Control::SIZE_EXPAND_FILL);
		filter_option->connect("em_selected", callable_mp(this, &ProjectManager::_on_order_option_changed));
		hb->add_child(filter_option);
		Vector<String> sort_filter_tles;
		sort_filter_tles.push_back(TTR("Last Eded"));
		sort_filter_tles.push_back(TTR("Name"));
		sort_filter_tles.push_back(TTR("Path"));
		sort_filter_tles.push_back(TTR("Tags"));
		for (int i = 0; i < sort_filter_tles.size(); i++) {
			filter_option->add_em(sort_filter_tles[i]);
		}
		search_panel = memnew(PanelContainer);
		search_panel->set_v_size_flags(Control::SIZE_EXPAND_FILL);
		search_tree_vb->add_child(search_panel);
		_project_list = memnew(ProjectList);
		_project_list->connect(ProjectList::SIGNAL_SELECTION_CHANGED, callable_mp(this, &ProjectManager::_update_project_buttons));
		_project_list->connect(ProjectList::SIGNAL_PROJECT_ASK_OPEN, callable_mp(this, &ProjectManager::_open_selected_projects_ask));
		_project_list->set_horizontal_scroll_mode(ScrollContainer::SCROLL_MODE_DISABLED);
		search_panel->add_child(_project_list);
	}
	{
		// Project tab side bar
		VBoxCoew(VBoxContainer);
		tree_vb->set_custom_minimum_size(Size2(120, 120));
		local_projects_hb->add_child(tree_vb);
		create_btn = memnew(Button);