### 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.
project_tags->set_custom_minimum_size(Vector2(0, 100) * EDSCALE);
		tag_vb->add_child(memnew(HSeparator));
		label = memnew(Label(TTR("All Tags")));
		tag_vb->add_child(label);
		label->set_theme_type_variation("HeaderMedium");
		label->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_CENTER);
		label = memnew(Label(TTR("Click tag to add  to the project.")));
		tag_vb->add_child(label);
		label->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_CENTER);
		all_tags = memnew(HFlowContainer);
		tag_vb->add_child(all_tags);
		all_tags->set_custom_minimum_size(Vector2(0, 100) * EDSCALE);
		tag_ed_error = memnew(Label);
		tag_vb->add_child(tag_ed_error);
		tag_ed_error->set_autowrap_mode(TextServer::AUTOWRAP_WORD);
		create_tag_nfirmationDialog);
		tag_manage_dialog->add_child(create_tag_dialog);
		create_tag_dialog->set_tle(TTR("Create New Tag"));
		create_tag_dialog->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_create_new_tag));
		tag_vb = memnew(VBoxContainer);
		create_tag_dialog->add_child(tag_vb);
		Label *info = memnew(Label(TTR("Tags are capalized automatically when displayed.")));
		tag_vb->add_child(info);
		new_tag_name = memnew(LineEd);
		tag_vb->add_child(new_tag_name);
		new_tag_name->connect("text_changed", callable_mp(this, &ProjectManager::_set_new_tag_name));
		new_tag_name->connect("text_submted", callable_mp(this, &ProjectManager::_create_new_tag).unbind(1));
		create_tag_dialog->connect("about_to_popup", callable_mp(new_tag_name, &LineEd::clear));
		create_tag_dialog->connect("about_to_popup", callable_mp((Control *)new_tag_name, &Control::grab_focus), CONNECT_DEFERRED);
		tag_error = memnew(Label);