### 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.
language_restart_as(ConfirmationDialog);
		language_restart_ask->set_ok_button_text(TTR("Restart Now"));
		language_restart_ask->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_restart_confirm));
		language_restart_ask->set_cancel_button_text(TTR("Continue"));
		add_child(language_restart_ask);
		scan_dir = memnew(EdorFileDialog);
		scan_dir->set_previews_enabled(false);
		scan_dir->set_access(EdorFileDialog::ACCESS_FILESYSTEM);
		scan_dir->set_file_mode(EdorFileDialog::FILE_MODE_OPEN_DIR);
		scan_dir->set_tle(TTR("Select a Folder to Scan")); // must be after mode or 's overridden
		scan_dir->set_current_dir(EDITOR_GET("filesystem/directories/default_project_path"));
		add_child(scan_dir);
		scan_dir->connect("dir_selected", callable_mp(this, &ProjectManager::_scan_begin));
		erase_missing_as(ConfirmationDialog);
		erase_missing_ask->set_ok_button_text(TTR("Remove All"));
		erase_missing_ask->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_erase_missing_projects_confirm));
		add_child(erase_missing_ask);
		erase_as(ConfirmationDialog);
		erase_ask->set_ok_button_text(TTR("Remove"));
		erase_ask->get_ok_button()->connect("pressed", callable_mp(this, &ProjectManager::_erase_project_confirm));
		add_child(erase_ask);
		VBoxContainer *erase_ask_vb = memnew(VBoxContainer);
		erase_ask->add_child(erase_ask_vb);
		erase_ask_label = memnew(Label);
		erase_ask_vb->add_child(erase_ask_label);
		// Comment out for now until we have a better warning system to
		// ensure users delete their project only.
		//delete_project_contents = memnew(CheckBox);
		//delete_project_contents->set_text(TTR("Also delete project contents (no undo!)"));
		//erase_ask_vb->add_child(delete_project_contents);