### 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 is a full, hard reload of the list. Don't call this unless really required, 's expensive.
	// If you have 150 projects,  may read through 150 files on your disk at once + load 150 icons.
	// Clear whole list
	for size(); ++i) {
		Item &project = _projects.wre[i];
		CRASH_COND(project.control == nullptr);
		memdelete(project.control); // Why not queue_free()?
	}
	_projects.clear();
	_last_clicked = "";
	_ss.clear();
	List<String> sections;
	_config.load(_config_path);
	_config.get_sections(&sections);
	for (const String &path : sections) {
		bool favore = _config.get_value(path, "favore", false);
		_projects.push_back(load_project_data(path, favore));
	}
	// Create controls
	for size(); ++i) {
		_create_project_em_control(i);
	}
	sort_projects();
	_update_icons_async();
	update_dock_menu();
	set_v_scroll(0);
}
void ProjectList::update_dock_menu() {