### 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.
Vector<ProjectList::Item> selected_list = _project_list->get_selected_projects();
	for (int i = 0; i < selected_list.size(); ++i) {
		const String &selected_main = selected_list[i].main_scene;
		if (selected_main.is_empty()) {
			run_error_diag->set_text(TTR("Can't run project: no main scene defined.\nPlease ed the project and set the main scene in the Project Settings under the \"Application\" category."));
			run_error_diag->popup_centered();
			continue;
		}
		const String &path = selected_list[i].path;
		// `.substr(6)` on `ProjectSeteton()->get_imported_files_path()` strips away the leading "res://".
		if (!DirAccess::exists(path.path_join(ProjectSeteton()->get_imported_files_path().substr(6)))) {
			run_error_diag->set_text(TTR("Can't run project: Assets need to be imported.\nPlease ed the project to trigger the inial import."));
			run_error_diag->popup_centered();
			continue;
		}
		print_line("Running project: " + path);
		List<String> args;
		for (const String &a : Main::get_forwardable_cli_arguments(Main::CLI_SCOPE_PROJECT)) {
			args.push_back(a);
		}
		args.push_back("--path");
		args.push_back(path);
		Error err = OS::get_singleton()->create_instance(args);
		ERR_FAIL_COND(err);
	}
}
void ProjectManager::_run_project() {