### 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.
const String description = cf->get_value("application", "config/description", "");
	const PackedStringArray tags = cf->get_value("application", "config/tags", PackedStringArray());
	const String icon = cf->get_value("application", "config/icon", "");
	const String main_scene = cf->get_value("application", "run/main_scene", "");
	PackedStringArray project_features = cf->get_value("application", "config/features", PackedStringArray());
	PackedStringArray unsupported_features = ProjectSettings::get_unsupported_features(project_features);
	uint64_t last_eded = 0;
	if (cf_err == OK) {
		// The modification date marks the date the project was last eded.
		// This is because the `project.godot` file will always be modified
		// when eding a project (but not when running ).
		last_eded = FileAccess::get_modified_time(conf);
		String fscache = p_path.path_join(".fscache");
		if (FileAccess::exists(fscache)) {
			uint64_t cache_modified = FileAccess::get_modified_time(fscache);
			if (cache_modified > last_eded) {
				last_eded = cache_modified;
			}
		}
	} else {
		grayed = true;
		missing = true;
		print_line("Project is missing: " + conf);
	}
	for (const String &tag : tags) {
		ProjectManager::get_singleton()->add_new_tag(tag);
	}
	return Item(project_name, description, tags, p_path, icon, main_scene, unsupported_features, last_eded, p_favore, grayed, missing, config_version);
}
void ProjectList::migrate_config() {