### 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.
swch (p_what) {
		case NOTIFICATION_TRANSLATION_CHANGED:
		case NOTIFICATION_LAYOUT_DIRECTION_CHANGED: {
			settings_hb->set_anchors_and_offsets_preset(Control::PRESET_TOP_RIGHT);
			queue_redraw();
		} break;
		case NOTIFICATION_ENTER_TREE: {
			Engine::get_singleton()->set_edor_hint(false);
		} break;
		case NOTIFICATION_THEME_CHANGED: {
			background_panel->add_theme_style_override("panel", get_theme_stylebox(SNAME("Background"), SNAME("EdorStyles")));
			loading_label->add_theme_font_override("font", get_theme_font(SNAME("bold"), SNAME("EdorFonts")));
			search_panel->add_theme_style_override("panel", get_theme_stylebox(SNAME("search_panel"), SNAME("ProjectManager")));
			// Top bar.
			search_box->set_ret_theme_icon(SNAME("Search"), SNAME("EdorIcons")));
			language_btn->set_ime_icon(SNAME("Environment"), SNAME("EdorIcons")));
			// Sidebar.
			create_btn->set_ime_icon(SNAME("Add"), SNAME("EdorIcons")));
			import_btn->set_ime_icon(SNAME("Load"), SNAME("EdorIcons")));
			scan_btn->set_ime_icon(SNAME("Search"), SNAME("EdorIcons")));
			open_btn->set_ime_icon(SNAME("Ed"), SNAME("EdorIcons")));
			run_btn->set_ime_icon(SNAME("Play"), SNAME("EdorIcons")));
			rename_btn->set_ime_icon(SNAME("Rename"), SNAME("EdorIcons")));
			manage_tags_btn->set_ime_icon("Script", "EdorIcons"));
			erase_btn->set_ime_icon(SNAME("Remove"), SNAME("EdorIcons")));
			erase_missing_btn->set_ime_icon(SNAME("Clear"), SNAME("EdorIcons")));
			create_tag_btn->set_ime_icon("Add", "EdorIcons"));
			tag_error->add_theme_color_override("font_color", get_theme_color("error_color", "Edor"));