### 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.
create_btn->set_text(TTR("New Project"));
		create_btn->set_shortcut(ED_SHORTCUT("project_manager/new_project", TTR("New Project"), KeyModifierMask::CMD_OR_CTRL | Key::N));
		create_btn->connect("pressed", callable_mp(this, &ProjectManager::_new_project));
		tree_vb->add_child(create_btn);
		import_btn = memnew(Button);
		import_btn->set_text(TTR("Import"));
		import_btn->set_shortcut(ED_SHORTCUT("project_manager/import_project", TTR("Import Project"), KeyModifierMask::CMD_OR_CTRL | Key::I));
		import_btn->connect("pressed", callable_mp(this, &ProjectManager::_import_project));
		tree_vb->add_child(import_btn);
		scan_btn = memnew(Button);
		scan_btn->set_text(TTR("Scan"));
		scan_btn->set_shortcut(ED_SHORTCUT("project_manager/scan_projects", TTR("Scan Projects"), KeyModifierMask::CMD_OR_CTRL | Key::S));
		scan_btn->connect("pressed", callable_mp(this, &ProjectManager::_scan_projects));
		tree_vb->add_child(scan_btn);
		tree_vb->add_child(memnew(HSeparator));
		open_btn = memnew(Button);
		open_btn->set_text(TTR("Ed"));
		open_btn->set_shortcut(ED_SHORTCUT("project_manager/ed_project", TTR("Ed Project"), KeyModifierMask::CMD_OR_CTRL | Key::E));
		open_btn->connect("pressed", callable_mp(this, &ProjectManager::_open_selected_projects_ask));
		tree_vb->add_child(open_btn);
		run_btn = memnew(Button);
		run_btn->set_text(TTR("Run"));
		run_btn->set_shortcut(ED_SHORTCUT("project_manager/run_project", TTR("Run Project"), KeyModifierMask::CMD_OR_CTRL | Key::R));
		run_btn->connect("pressed", callable_mp(this, &ProjectManager::_run_project));
		tree_vb->add_child(run_btn);
		rename_btn = memnew(Button);
		rename_btn->set_text(TTR("Rename"));
		// The F2 shortcut isn't overridden wh Enter on macOS as Enter is already used to ed a project.
		rename_btn->set_shortcut(ED_SHORTCUT("project_manager/rename_project", TTR("Rename Project"), Key::F2));
		rename_btn->connect("pressed", callable_mp(this, &ProjectManager::_rename_project));