### 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_needs_reload = false;
	// The default project icon is 128×128 to look crisp on hiDPI displays,
	// but we want the actual displayed size to be 64×64 on loDPI displays.
	project_icon->set_expand_mode(TextureRect::EXPAND_IGNORE_SIZE);
	project_icon->set_custom_minimum_size(Size2(64, 64) * EDSCALE);
	project_icon->set_stretch_mode(TextureRect::STRETCH_KEEP_ASPECT_CENTERED);
	project_icon->set_texture(p_icon);
}
:set_unsupported_features(const PackedStringArray &p_features) {
	if (p_features.size() > 0) {
		String unsupported_features_str = String(", ").join(p_features);
		project_unsupported_features->set_tooltip_text(TTR("The project uses features unsupported by the current build:") + "\n" + unsupported_features_str);
		project_unsupported_features->show();
	} else {
		project_unsupported_features->hide();
	}
}
bool ProjectListItemControl::should_load_project_icon() const {
	return icon_needs_reload;
}
:set_selected(bool p_selected) {
	is_selected = p_selected;
	queue_redraw();
}
:set_is_favore(bool p_favore) {
	favore_button->set_modulate(p_favore ? Color(1, 1, 1, 1) : Color(1, 1, 1, 0.2));
}
:set_is_missing(bool p_missing) {