A couple of off the top of my head thoughts…
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Have you confirmed the issue is specific to the iPad/IOS by trying a different device (Windows laptop, iPhone etc)?
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You mentioned “I can use a port scanner on the iPad, while connected to one of the router’s wifi networks”. Is the router WiFi network the iPad connects to on the same subnet that the NUC is on? I recall reading that Roon is unable to be discovered across different subnets(?)