### 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 = p_path.simplify_path();
	project_path->set_text(sp);
	_path_text_changed(sp);
	get_ok_button()->call_deferred(SNAME("grab_focus"));
}
void ProjectDialog::_install_path_selected(const String &p_path) {
	String sp = p_path.simplify_path();
	install_path->set_text(sp);
	_path_text_changed(sp);
	get_ok_button()->call_deferred(SNAME("grab_focus"));
}
void ProjectDialog::_browse_path() {
	fdialog->set_current_dir(project_path->get_text());
	if (mode == MODE_IMPORT) {
		fdialog->set_file_mode(EdorFileDialog::FILE_MODE_OPEN_FILE);
		fdialog->clear_filters();
		fdialog->add_filter("project.godot", vformat("%s %s", VERSION_NAME, TTR("Project")));
		fdialog->add_filter("*.zip", TTR("ZIP File"));
	} else {
		fdialog->set_file_mode(EdorFileDialog::FILE_MODE_OPEN_DIR);
	}
	fdialog->popup_file_dialog();
}
void ProjectDialog::_browse_install_path() {
	fdialog_install->set_current_dir(install_path->get_text());
	fdialog_install->set_file_mode(EdorFileDialog::FILE_MODE_OPEN_DIR);
	fdialog_install->popup_file_dialog();
}
void ProjectDialog::_create_folder() {