Java Edition in 1.20+
This minecart network system allows automatically routing from any station to any station while running.
Max 27 stations can be built.
Pick up a item that selects station in minecart with chest, and push a button for departing.(Don't shuffle items in minecart with chest)

System mechanism
This system is composed of 3 detection method.

First method detects whether you chose next station or not. Minecart with chest is sent an immaterial item to and filled in the blank. Then, attempting whether next item can be sent or not detects the item whether you chose or not. This means if the item cannot be sent, minecart goes toward the station you chose, if not, the direction is to next stations.

Second method can detect whether the number you selected is upper or lower from any number. Items in chest are aligned and numbered.(from top on left to right, then down and back left...) Chest is sent a station item and tries to be sent next an immaterial item. Succession of sending the immaterial item means the item you chose is upper from the station item in junction.

Third method is combination of 2 upper lower detectors. Send (A) station item, send (B), extract (A), send (I), extract (I), extract(B), and detect immaterial (I) item can be sent or not.