### 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.
String sp = _test_path();
	if (!sp.is_empty()) {
		
		if (project_name->get_text().strip_edges().is_empty() || project_name->get_text().strip_edges() == TTR("New Game Project")) {
			sp = sp.replace("\\", "/");
			int lidx = sp.rfind("/");
			if (lidx != -1) {
				sp = sp.substr(lidx + 1, sp.length()).capalize();
			}
			if (sp.is_empty() && mode == MODE_IMPORT) {
				sp = TTR("Imported Project");
			}
			project_name->set_text(sp);
			_text_changed(sp);
		}
	}
	if (!created_folder_path.is_empty() && created_folder_path != p_path) {
		_remove_created_folder();
	}
}
void ProjectDialog::_file_selected(const String &p_path) {