If you're using Spigot nothing changes for you. You can keep using the jar named worldborderapi-1.205.0.jar

If you are on Paper you can use the Mojang mapped jar worldborderapi-1.205.0-dev.jar now, as Paper can handle these in 1.20.5 and up.
Funfact: Due to the state that the internal didn't change for a long time for worldborder related things, you can even use the dev jar on future versions.