### 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.
for (int i = 0; i < unsupported_features.size(); i++) {
			String feature = unsupported_features[i];
			if (feature == "Double Precision") {
				warning_message += TTR("Warning: This project uses double precision floats, but this version of\nGodot uses single precision floats. Opening this project may cause data loss.\n\n");
				unsupported_features.remove_at(i);
				i--;
			} else if (feature == "C#") {
				warning_message += TTR("Warning: This project uses C#, but this build of Godot does not have\nthe Mono module. If you proceed you will not be able to use any C# scripts.\n\n");
				unsupported_features.remove_at(i);
				i--;
			} else if (feature.substr(0, 3).is_numeric()) {
				warning_message += vformat(TTR("Warning: This project was built in Godot %s.\nOpening will upgrade or downgrade the project to Godot %s.\n\n"), Variant(feature), Variant(VERSION_BRANCH));
				unsupported_features.remove_at(i);
				i--;
			}
		}
		if (!unsupported_features.is_empty()) {
			String unsupported_features_str = String(", ").join(unsupported_features);
			warning_message += vformat(TTR("Warning: This project uses the following features not supported by this build of Godot:\n\n%s\n\n"), unsupported_features_str);
		}
		warning_message += TTR("Open anyway? Project will be modified.");
		ask_update_label->set_horizontal_alignment(HORIZONTAL_ALIGNMENT_CENTER);
		ask_update_settings->set_text(warning_message);
		ask_update_settings->popup_centered(popup_min_size);
		return;
	}
	// Open if the project is up-to-date.
	_open_selected_projects();
}
void ProjectManager::_full_convert_button_pressed() {