In Linux the configuration is kept in ~/.config/kopia/ and the cache in ~/.cache/kopia/.
You could make copies of the config when connected to different repo’s and have a script to stop kopia server and kopia-ui and copy the wanted repo config back.
I’m not sure about copying the cache or keeping it.
I’m not sure if it’s the same in Linux, but in Windows you right click the tray icon, and there you have the option to connect to another repository. All the connected repositories will then be available through the tray icon menu.