As dumb as it sounds with how cryptic apple errors usually are, the error response is literal. The request took too long, as for what it took too long that is usually a network related issue. There are a lot of API commands that go back and forth for VPP app installs, something is getting filtered, blocked or any number of random network things done to it.
My suggestion: Download the Mac Evaluation Utility and run it on an impacted device and check for TLS filtering, and blocked ports.
