The address changes for advertising purposes, but once a connection is made and maintained, you don't need to worry about re-establishing it. The address of the peer is given to us when the connection is established, but we don't do anything with it. It is not clear to me if this address can change or not. It is a public address, but I am not sure whether it changes. I have been studying material from
https://devzone.nordicsemi.com/ and the API docs, and some other material. I am not an expert on all this at all, and it would be worth your studying some material on all this.
It might be that you need to rely on the IRK (not the address) to identify the central you are talking to.
Perhaps there are some examples associated with the Nordic SDK or the Arduino nRF library that show how to distinguish multiple centrals. We could add a feature to return the address or some other data from the connection. I am sorry I cannot be authoritative on this.
The UARTService requires no pairing (and is less secure because of that).