### 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.
version_btn = memnew(LinkButton);
		String hash = String(VERSION_HASH);
		if (hash.length() != 0) {
			hash = " " + vformat("[%s]", hash.left(9));
		}
		version_btn->set_text("v" VERSION_FULL_BUILD + hash);
		// Fade the version label to be less prominent, but still readable.
		version_btn->set_self_modulate(Color(1, 1, 1, 0.6));
		version_btn->set_underline_mode(LinkButton::UNDERLINE_MODE_ON_HOVER);
		version_btn->set_tooltip_text(TTR("Click to copy."));
		version_btn->connect("pressed", callable_mp(this, &ProjectManager::_version_button_pressed));
		spacer_vb->add_child(version_btn);
		// Add a small horizontal spacer between the version and language buttons
		// to distinguish them.
		Controntrol);
		settings_hb->add_child(h_spacer);
		language_btn = memnew(OptionButton);
		language_btn->set_focus_mode(Control::FOCUS_NONE);
		language_btn->set_f_to_longest_em(false);
		language_btn->set_flat(true);
		language_btn->connect("em_selected", callable_mp(this, &ProjectManager::_language_selected));
#ifdef ANDROID_ENABLED
		// The language selection dropdown doesn't work on Android (as the setting isn't saved), see GH-60353.
		// Also, the dropdown  spawns is very tall and can't be scrolled whout a hardware mouse.
		// Hiding the language selection dropdown also leaves more space for the version label to display.
		language_btn->hide();
#endif
		Vector<String> edor_languages;
		List<PropertyInfo> edor_settings_properties;
		EdorSeteton()->get_property_list(&edor_settings_properties);