Through hole via isolation in Eagle CAD 4 layers board
You don't need to worry about it since your netlist will take care of that. If your via passes through a plane or copper pour that is not in the same net, a cutout will be made around the hole in the plane so the via does not make contact. These cutouts might not appear until you actually connect your polygon to a net.

It's almost the exact same thing as routing a trace through a polygon or copper pour that is connected to a different net. Cutouts will be made in the polygon around the trace.

It should take ZERO additional steps on your part. Just route as normal.

Can you imagine having to deal with that manually on a board with hundreds or thousands of vias? And with modifications that could occur? Any software that did not automate that would immediately die even if it was free.