### 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.
add_theme_constant_override(SNAME("separation"), 0);
	set_v_size_flags(SIZE_SHRINK_CENTER);
	tag_string = p_text;
	display_close = p_display_close;
	Color tag_color = Color(1, 0, 0);
	tag_color.set_ok_hsl_s(0.8);
	tag_color.set_ok_hsl_h(float(p_text.hash() * 10001 % UINT32_MAX) / float(UINT32_MAX));
	set_self_modulate(tag_color);
	ColorRect *cr = memnew(ColorRect);
	add_child(cr);
	cr->set_custom_minimum_size(Vector2(4, 0) * EDSCALE);
	cr->set_color(tag_color);
	button = memnew(Button);
	add_child(button);
	button->set_auto_translate(false);
	button->set_text(p_text.capalize());
	button->set_focus_mode(FOCUS_NONE);
	button->set_icon_alignment(HORIZONTAL_ALIGNMENT_RIGHT);
	button->set_theme_type_variation(SNAME("ProjectTag"));
}
void ProjectTag::connect_button_to(const Callable &p_callable) {
	button->connect(SNAME("pressed"), p_callable, CONNECT_DEFERRED);
}
const String ProjectTag::get_tag() const {
	return tag_string;
}