### 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.
npdialog->set_mode(ProjectDialog::MODE_IMPORT);
	npdialog->show_dialog();
}
void ProjectManager::_rename_project() {
	const HashSet<String> &selected_list = _project_list->get_selected_project_keys();
	if (selected_list.size() == 0) {
		return;
	}
	for (const String &E : selected_list) {
		npdialog->set_project_path(E);
		npdialog->set_mode(ProjectDialog::MODE_RENAME);
		npdialog->show_dialog();
	}
}
void ProjectManager::_manage_project_tags() {
	for (int i = 0; i < project_tags->get_child_count(); i++) {
		project_tags->get_child(i)->queue_free();
	}
	const ProjectList::Item em = _project_list->get_selected_projects()[0];
	current_project_tags = em.tags;
	for (const String &tag : current_project_tags) {
		ProjectTag *tag_control = memnew(ProjectTag(tag, true));
		project_tags->add_child(tag_control);
		tag_control->connect_button_to(callable_mp(this, &ProjectManager::_delete_project_tag).bind(tag));
	}
	tag_ed_error->hide();
	tag_manage_dialog->popup_centered(Vector2i(500, 0) * EDSCALE);
}
void ProjectManager::_add_project_tag(const String &p_tag) {