### 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.
if (_projects[i].path == dir_path) {
				if (was_selected) {
					select_project(i);
					ensure_project_visible(i);
				}
				_load_project_icon(i);
				index = i;
				break;
			}
		}
	}
	return index;
}
void ProjectList::add_project(const String &dir_path, bool favore) {
	if (!_config.has_section(dir_path)) {
		_config.set_value(dir_path, "favore", favore);
	}
}
void ProjectList::save_config() {
	_config.save(_config_path);
}
void ProjectList::set_project_version(const String &p_project_path, int p_version) {
	for (ProjectList::Item &E : _projects) {
		if (E.path == p_project_path) {
			E.version = p_version;
			break;
		}
	}
}
int ProjectList::get_project_count() const {