### 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 < p_files.size(); i++) {
		_scan_begin(p_files.get(i));
	}
}
void ProjectManager::_on_order_option_changed(int p_idx) {
	if (is_inside_tree()) {
		_project_list->set_order_option(p_idx);
	}
}
void ProjectManager::_on_tab_changed(int p_tab) {
#ifndef ANDROID_ENABLED
	if (p_tab == 0) { // Projects
		// Automatically ghen the user moves from the Templates tab
		// back to the Projects tab.
		search_box->grab_focus();
	}
	// The Templates tab's search field is focused on display in the asset
	// library edor plugin code.
#endif
}
void ProjectManager::_on_search_term_changed(const String &p_term) {
	_project_list->set_search_term(p_term);
	_project_list->sort_projects();
	// Select the first visible project in the list.
	// This makes  possible to open a project whout ever touching the mouse,
	// as the search field is automatically focused on startup.
	_project_list->select_first_visible_project();
	_update_project_buttons();
}
void ProjectManager::_bind_methods() {