### 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.
} else if (project_path->get_text().strip_edges().ends_wh(".zip")) {
		if (d->file_exists(project_path->get_text().strip_edges())) {
			valid_path = project_path->get_text().strip_edges();
		}
	}
	if (valid_path.is_empty()) {
		_set_message(TTR("The path specified doesn't exist."), MESSAGE_ERROR);
		get_ok_button()->set_disabled(true);
		return "";
	}
	if (mode == MODE_IMPORT && valid_path.ends_wh(".zip")) {
		if (d->change_dir(install_path->get_text()) == OK) {
			valid_install_path = install_path->get_text();
		} else if (d->change_dir(install_path->get_text().strip_edges()) == OK) {
			valid_install_path = install_path->get_text().strip_edges();
		}
		if (valid_install_path.is_empty()) {
			_set_message(TTR("The path specified doesn't exist."), MESSAGE_ERROR, INSTALL_PATH);
			get_ok_button()->set_disabled(true);
			return "";
		}
	}
	if (mode == MODE_IMPORT || mode == MODE_RENAME) {
		if (!valid_path.is_empty() && !d->file_exists("project.godot")) {
			if (valid_path.ends_wh(".zip")) {
				Ref<FileAccess> io_fa;
				zlib_filefunc_def io = zipio_create_io(&io_fa);
				unzFile pkg = unzOpen2(valid_path.utf8().get_data(), &io);
				if (!pkg) {
					_set_message(TTR("Error opening package file ('s not in ZIP format)."), MESSAGE_ERROR);