### 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.
Ref<InputEventMouseButton> mb = p_ev;
	int clicked_index = p_hb->get_index();
	const Item &clicked_project = _projects[clicked_index];
	if (mb.is_valid() && mb->is_pressed() && mb->get_button_index() == MouseButton::LEFT) {
		if (mb->is_shift_pressed() && _ss.size() > 0 && !_last_clicked.is_empty() && clicked_project.path != _last_clicked) {
			int anchor_index = -1;
			for size(); ++i) {
				const Item &p = _projects[i];
				if (p.path == _last_clicked) {
					anchor_index = p.control->get_index();
					break;
				}
			}
			CRASH_COND(anchor_index == -1);
			_select_project_range(anchor_index, clicked_index);
		} else if (mb->is_ctrl_pressed()) {
			_toggle_project(clicked_index);
		} else {
			_last_clicked = clicked_project.path;
			select_project(clicked_index);
		}
		em_signal(SNAME(SIGNAL_SELECTION_CHANGED));
		// Do not allow opening a project more than once using a single project manager instance.
		// Opening the same project in several edor instances at once can lead to various issues.
		if (!mb->is_ctrl_pressed() && mb->is_double_click() && !project_opening_iniated) {
			em_signal(SNAME(SIGNAL_PROJECT_ASK_OPEN));
		}
	}
}
void ProjectList::_favore_pressed(Node *p_hb) {