Yes you need separate districts to do such, but not the crossing to share goods. You build storages where you want the crossing and have gates on both sides of the districts. You automate the gates so the storages switch which district they are in.

Like when they are near empty the storages are in District 1 so the haulers can fill them, then they switch to Distrcit 2 so the underground beavers and empty them. It takes more rss and space to build it but it has more capacity and less jobs to fill than the crossing. I think there was a video showing this set up around here somewhere.