### 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.
multi_open_as(ConfirmationDialog);
		multi_open_ask->set_ok_button_text(TTR("Ed"));
		multi_open_ask->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_open_selected_projects));
		add_child(multi_open_ask);
		multi_run_as(ConfirmationDialog);
		multi_run_ask->set_ok_button_text(TTR("Run"));
		multi_run_ask->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_run_project_confirm));
		add_child(multi_run_ask);
		multi_scan_as(ConfirmationDialog);
		multi_scan_ask->set_ok_button_text(TTR("Scan"));
		add_child(multi_scan_ask);
		ask_update_settings = memnew(ConfirmationDialog);
		ask_update_settings->set_autowrap(true);
		ask_update_settings->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_confirm_update_settings));
		full_convert_button = ask_update_settings->add_button(TTR("Convert Full Project"), !GLOBAL_GET("gui/common/swap_cancel_ok"));
		full_convert_button->connect("pressed", callable_mp(this, &ProjectManager::_full_convert_button_pressed));
		add_child(ask_update_settings);
		ask_full_convert_nfirmationDialog);
		ask_full_convert_dialog->set_autowrap(true);
		ask_full_convert_dialog->set_text(TTR("This option will perform full project conversion, updating scenes, resources and scripts from Godot 3.x to work in Godot 4.0.\n\nNote that this is a best-effort conversion, i.e.  makes upgrading the project easier, but  will not open out-of-the-box and will still require manual adjustments.\n\nIMPORTANT: Make sure to backup your project before converting, as this operation makes  impossible to open  in older versions of Godot."));
		ask_full_convert_dialog->connect("confirmed", callable_mp(this, &ProjectManager::_perform_full_project_conversion));
		add_child(ask_full_convert_dialog);
		npdialog = memnew(ProjectDialog);
		npdialog->connect("projects_updated", callable_mp(this, &ProjectManager::_on_projects_updated));
		npdialog->connect("project_created", callable_mp(this, &ProjectManager::_on_project_created));
		add_child(npdialog);
		run_error_diag = memnew(AcceptDialog);
		run_error_diag->set_tle(TTR("Can't run project"));
		add_child(run_error_diag);
		dialog_error = memnew(AcceptDialog);