App is trying to search my network

Forums are mostly answered by other members.
You could open a ticket with support to ask.

I could be wrong but I'm pretty sure that doesn't happen.

It's pretty much impossible with a network scan to determine what is running on a different device, without getting full access to those devices. As I said, I'm pretty sure that's not happening with the app.
“Apps that access your local network can collect information about nearby devices in order to determine which networks you join and when. This information could be used to create a profile of you.”
So the chess.com phone app can identify chess engine sites being used by other devices on my network. It is pretty clear to me that is part of the cheat prevention.
Why are you trying so hard, giving false information, on something you clearly don’t understand?

“Apps that access your local network can collect information about nearby devices in order to determine which networks you join and when. This information could be used to create a profile of you.”
So the chess.com phone app can identify chess engine sites being used by other devices on my network. It is pretty clear to me that is part of the cheat prevention.
Why are you trying so hard, giving false information, on something you clearly don’t understand?
An app could get IP data potentially from your network, but the way networks actually work, it would only be able to see broadcast traffic that makes it to your device, since any other traffic would not be routed to your device.
I'm providing information based on experience and how networking traffic works. Again, I'm pretty sure that's not being done, but if you think it is, then I guess that's all there is ...

Go Into your Phones settings you will See which Apps are allowed what you can disable THIS Apps Access there
Why is the app trying to do that?