Tried your steps with several variations (saving as “Xojo binary project”, “Xojo mxl project” or “Xojo project”; creating a new folder with either the button or “Command-N”). Never got a hang nor something unexpected.
What’s your IDE and OS version?
Anything special in the path to your folder?
What if you create the folder from the Finder while the save dialog is open?
Looks like a file system issue, no?
Have you tried on a completely different volume/disk? Even a server.
Even if Xojo is the only app having this issue, it still can be related to something about your file system, so I’d rule this out by saving on another, very different, location with the same steps.
Are some of them remote volumes?
In the other way around, do you happen to have another computer on the same network from which you could try remote connecting (using file sharing) and trying from there?
You may also make a temporary new user account on your computer to test whether your account may have a corruption, but that’s perhaps too early to try…