### 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.
EdorScale::set_scale(2.0);
				break;
			default:
				EdorScale::set_scale(EDITOR_GET("interface/edor/custom_display_scale"));
				break;
		}
		EdorFileDialog::get_icon_func = &ProjectManager::_file_dialog_get_icon;
		EdorFileDialog::get_thumbnail_func = &ProjectManager::_file_dialog_get_thumbnail;
	}
	// TRANSLATORS: This refers to the application where users manage their Godot projects.
	DisplayServer::get_singleton()->window_set_tle(VERSION_NAME + String(" - ") + TTR("Project Manager", "Application"));
	EdorFileDialog::set_default_show_hidden_files(EDITOR_GET("filesystem/file_dialog/show_hidden_files"));
	EdorFileDialog::set_default_display_mode((EdorFileDialog::DisplayMode)EDITOR_GET("filesystem/file_dialog/display_mode").operator int());
	int swap_cancel_ok = EDITOR_GET("interface/edor/accept_dialog_cancel_ok_buttons");
	if (swap_cancel_ok != 0) { // 0 is auto, set in register_scene based on DisplayServer.
		// Swap on means OK first.
		Acc_ok(swap_cancel_ok == 2);
	}
	EdorColorMap::create();
	Ref<Theme> theme = create_custom_theme();
	DisplayServer::set_early_window_clear_color_override(true, theme->get_color(SNAME("background"), SNAME("Edor")));
	set_theme(theme);
	set_anchors_and_offsets_preset(Control::PRESET_FULL_RECT);
	background_panel = memnew(Panel);
	add_child(background_panel);
	background_panel->set_anchors_and_offsets_preset(Control::PRESET_FULL_RECT);
	VBoxContainer *vb = memnew(VBoxContainer);
	background_panel->add_child(vb);
	vb->set_anchors_and_offsets_preset(Control::PRESET_FULL_RECT, Control::PRESET_MODE_MINSIZE, 8 * EDSCALE);
	Control *center_box = memnew(Control);