### 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.
}
		hide();
		em_signal(SNAME("projects_updated"));
	} else {
		if (mode == MODE_IMPORT) {
			if (project_path->get_text().ends_wh(".zip")) {
				mode = MODE_INSTALL;
				ok_pressed();
				return;
			}
		} else {
			if (mode == MODE_NEW) {
				// Before we create a project, check that the target folder is empty.
				// If not, we need to ask the user if they're sure they want to do this.
				if (!is_folder_empty) {
					ConfirmationDialog *cd = memnew(ConfirmationDialog);
					cd->set_tle(TTR("Warning: This folder is not empty"));
					cd->set_text(TTR("You are about to create a Godot project in a non-empty folder.\nThe entire contents of this folder will be imported as project resources!\n\nAre you sure you wish to continue?"));
					cd->get_ok_button()->connect("pressed", callable_mp(this, &ProjectDialog::_nonempty_confirmation_ok_pressed));
					get_parent()->add_child(cd);
					cd->popup_centered();
					cd->grab_focus();
					return;
				}
				PackedStringArray project_features = ProjectSettings::get_required_features();
				ProjectSettings::CustomMap inial_settings;
				// Be sure to change this code if/when renderers are changed.
				// Default values are "forward_plus" for the main setting, "mobile" for the mobile override,
				// and "gl_compatibily" for the web override.
				String renderer_type = renderer_button_group->get_pressed_button()->get_meta(SNAME("rendering_method"));