### 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.
// This method must be called before calling `get_tree()->qu()`.
	// Otherwise, s effect won't be visible
	// Dim the project manager window while 's quting to make  clearer that 's busy.
	// No transion is applied, as the effect needs to be visible immediately
	float c = 0.5f;
	Color dim_color = Color(c, c, c);
	set_modulate(dim_color);
}
void ProjectManager::_update_project_buttons() {
	Vector<ProjectList::Item> selected_projects = _project_list->get_selected_projects();
	bool empty_selection = selected_projects.is_empty();
	bool is_missing_project_selected = false;
	for (int i = 0; i < selected_projects.size(); ++i) {
		if (selected_projects[i].missing) {
			is_missing_project_selected = true;
			break;
		}
	}
	erase_btn->set_disabled(empty_selection);
	open_btn->set_disabled(empty_selection || is_missing_project_selected);
	rename_btn->set_disabled(empty_selection || is_missing_project_selected);
	manage_tags_btn->set_disabled(empty_selection || is_missing_project_selected || selected_projects.size() > 1);
	run_btn->set_disabled(empty_selection || is_missing_project_selected);
	erase_missing_btn->set_disabled(!_project_list->is_any_project_missing());
}
void ProjectManager::shortcut_input(const Ref<InputEvent> &p_ev) {