### 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_MOUSE_EXIT: {
			is_hovering = false;
			queue_redraw();
		} break;
		case NOTIFICATION_DRAW: {
			if (is_selected) {
				draw_style_box(get_theme_stylebox(SNAME("selected"), SNAME("Tree")), Rect2(Point2(), get_size()));
			}
			if (is_hovering) {
				draw_style_box(get_theme_stylebox(SNAME("hover"), SNAME("Tree")), Rect2(Point2(), get_size()));
			}
			draw_line(Point2(0, get_size().y + 1), Point2(get_size().x, get_size().y + 1), get_theme_color(SNAME("guide_color"), SNAME("Tree")));
		} break;
	}
}
:set_project_tle(const String &p_tle) {
	project_tle->set_text(p_tle);
}
:set_project_path(const String &p_path) {
	project_path->set_text(p_path);
}
:set_tags(const PackedStringArray &p_tags, ProjectList *p_parent_list) {
	for (const String &tag : p_tags) {
		ProjectTag *tag_control = memnew(ProjectTag(tag));
		tag_container->add_child(tag_control);
		tag_control->connect_button_to(callable_mp(p_parent_list, &ProjectList::add_search_tag).bind(tag));
	}
}
:set_project_icon(const Ref<Texture2D> &p_icon) {