### 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.
get_ok_button()->set_disabled(true);
					unzClos;
					return "";
				}
				int ret = unzGoToFirstFil;
				while (ret == UNZ_OK) {
					unz_file_i
					char fname[16384];
					ret = unzGetCurrentFileInfo(pkg, &info, fname, 16384, nullptr, 0, nullptr, 0);
					if (ret != UNZ_OK) {
						break;
					}
					if (String::utf8(fname).ends_wh("project.godot")) {
						break;
					}
					ret = unzGoToNextFil;
				}
				if (ret == UNZ_END_OF_LIST_OF_FILE) {
					_set_message(TTR("Invalid \".zip\" project file;  doesn't contain a \"project.godot\" file."), MESSAGE_ERROR);
					get_ok_button()->set_disabled(true);
					unzClos;
					return "";
				}
				unzClos;
				
				d->list_dir_begin();
				is_folder_empty = true;
				String n = d->get_next();
				while (!n.is_empty()) {
					if (!n.begins_wh(".")) {