### 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.
inial_settings["rendering/renderer/rendering_method"] = renderer_type;
				EdorSeteton()->set("project_manager/default_renderer", renderer_type);
				EdorSeteton()->save();
				if (renderer_type == "forward_plus") {
					project_features.push_back("Forward Plus");
				} else if (renderer_type == "mobile") {
					project_features.push_back("Mobile");
				} else if (renderer_type == "gl_compatibily") {
					project_features.push_back("GL Compatibily");
					// Also change the default rendering method for the mobile override.
					inial_settings["rendering/renderer/rendering_method.mobile"] = "gl_compatibily";
				} else {
					WARN_PRINT("Unknown renderer type. Please report this as a bug on GHub.");
				}
				project_features.sort();
				inial_settings["application/config/features"] = project_features;
				inial_settings["application/config/name"] = project_name->get_text().strip_edges();
				inial_settings["application/config/icon"] = "res://icon.svg";
				if (ProjectSeteton()->save_custom(dir.path_join("project.godot"), inial_settings, Vector<String>(), false) != OK) {
					_set_message(TTR("Couldn't create project.godot in project path."), MESSAGE_ERROR);
				} else {
					// Store default project icon in SVG format.
					Error err;
					Ref<FileAccess> fa_icon = FileAccess::open(dir.path_join("icon.svg"), FileAccess::WRITE, &err);
					fa_icon->store_string(get_default_project_icon());
					if (err != OK) {
						_set_message(TTR("Couldn't create icon.svg in project path."), MESSAGE_ERROR);
					}
					EdorVCSInterface::create_vcs_metadata_files(EdorVCSInterface::VCSMetadata(vcs_metadata_selection->get_selected()), dir);
				}