### 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.
_icon_load_index = 0;
	set_process(true);
}
void ProjectList::_load_project_icon(int p_index) {
	Item &em = _pro_index];
	Ref<Texture2D> default_icon = get_theme_icon(SNAME("DefaultProjectIcon"), SNAME("EdorIcons"));
	Ref<Texture2D> icon;
	if (!em.icon.is_empty()) {
		Ref<Image> img;
		img.instantiate();
		Error err = img->load(em.icon.replace_first("res://", em.path + "/"));
		if (err == OK) {
			img->resize(default_icon->get_width(), default_icon->get_height(), Image::INTERPOLATE_LANCZOS);
			icon = ImageTexture::create_from_image(img);
		}
	}
	if (icon.is_null()) {
		icon = default_icon;
	}
	em.control->set_project_icon(icon);
}
// Load project data from p_property_key and return  in a ProjectList::Item.
// p_favore is passed directly into the Item.
ProjectList::Item ProjectList::load_project_data(const String &p_path, bool p_favore) {