I answered my own issue, and thought maybe somebody else could use this: My app has the UDP Multicast entitlement, and I assumed all the hoops I'd jumped through to get that running was adequate, and before iOS 18, it was. With iOS 18, I also needed to specifically have an info.plist entry for Privacy - Local Network Usage Description because without it the user would not be prompted for their permission. With it, it all works again.

I do not have any control over an app which runs on a computer, while MY APP uses UDP to communicate with the third party app. I cannot choose another type of implementation, and I have an older iPad running iPadOS 16.7.10 that still functions properly, while my iOS 18.x devices do not. Is this problem being addressed, or is the app I spent 6 months making in order to take advantage of pre-defined inter-app communication now useless?