I have tested your example with Xcode 13.2.1 on iOS 15.2. I've got the Local Network Privacy Prompt and the request went through successfully.
However, the test you are using is not reflecting the original issue since the local network request is performed by the main application (that works as expected). What doesn't work is making the local network request from the UI Testing Bundle (URLSessionExampleUITests in your example).
ac.ciobanu
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I stand corrected, this issue hasn't been fixed yet (re-tested using Xcode 13.2.1)