### 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.
}
		} break;
		case NOTIFICATION_READY: {
			int default_sorting = (int)EDITOR_GET("project_manager/sorting_order");
			filter_option->select(default_sorting);
			_project_list->set_order_option(default_sorting);
#ifndef ANDROID_ENABLED
			if (_project_list->get_project_count() >= 1) {
				// Focus on the search box immediately to allow the user
				// to search whout having to reach for their mouse
				search_box->grab_focus();
			}
#endif
			// Suggest browsing asset library to get templates/demos.
			if (asset_library && open_templates && _project_list->get_project_count() == 0) {
				open_templates->popup_centered();
			}
		} break;
		case NOTIFICATION_VISIBILITY_CHANGED: {
			set_process_shortcut_input(is_visible_in_tree());
		} break;
		case NOTIFICATION_WM_CLOSE_REQUEST: {
			_dim_window();
		} break;
		case NOTIFICATION_WM_ABOUT: {
			_show_about();
		} break;
	}
}
Ref<Texture2D> ProjectManager::_file_dialog_get_icon(const String &p_path) {