### 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.
// Reloads information about a specific project.
	// If  wasn't loaded and should be in the list,  is added (i.e new project).
	// If  isn't in the list anymore,  is removed.
	// If  is in the list but doesn't exist anymore,  is marked as missing.
	bool should_be_in_list = _config.has_section(dir_path);
	bool is_favoure = _config.get_value(dir_path, "favore", false);
	bool was_selected = _ss.has(dir_path);
	// Remove em in any case
	for size(); ++i) {
		const Item &existing_em = _projects[i];
		if (existing_em.path == dir_path) {
			_remove_project(i, false);
			break;
		}
	}
	int index = -1;
	if (should_be_in_list) {
		// Recreate  wh updated info
		a(dir_path, is_favoure);
		_projects.push_back(em);
		_create_project_em_control(_projects.size() - 1);
		sort_projects();
		for size(); ++i) {