### 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.
w->set_min_size(Size2(520, 350) * EDSCALE);
	}
	// Resize the bootsplash window based on Edor display scale EDSCALE.
	float scale_factor = MAX(1, EDSCALE);
	if (scale_factor > 1.0) {
		Vector2i window_size = DisplayServer::get_singleton()->window_get_size();
		Rect2i screen_rect = DisplayServer::get_singleton()->screen_get_usable_rect(DisplayServer::get_singleton()->window_get_current_screen());
		window_size *= scale_factor;
		DisplayServer::get_singleton()->window_set_size(window_size);
		if (screen_rect.size != Vector2i()) {
			Vector2i window_posion;
			window_posion.x = screen_rect.posion.x + (screen_rect.size.x - window_size.x) / 2;
			window_posion.y = screen_rect.posion.y + (screen_rect.size.y - window_size.y) / 2;
			DisplayServer::get_singleton()->window_set_posion(window_posion);
		}
	}
	OS::get_singleton()->set_low_processor_usage_mode(true);
}
ProjectManager::~ProjectManager() {
	singleton = nullptr;
	if (EdorSeteton()) {
		EdorSettings::destroy();
	}
}
void ProjectTag::_notification(int p_what) {
	if (display_close && p_what == NOTIFICATION_THEME_CHANGED) {
		button->set_ime_icon(SNAME("close"), SNAME("TabBar")));
	}
}
ProjectTag::ProjectTag(const String &p_text, bool p_display_close) {