Your routes, collections and landmarks sync automatically through iCloud. Every device signed in to the same Apple Account gets them. Plan a route on the Mac and it is on the phone before you leave. There is no file to copy and no folder to find.
Your library is therefore not trapped on one device. If a phone is lost or replaced, sign the new one in. The library comes back.
The iCloud Sync panel shows the current state. It reports syncing, up to date, or when the last change arrived. Use Sync Now to push something immediately instead of waiting.
If the panel says you are not signed in to iCloud, nothing is syncing. Sign in, and the library uploads from there.
Sync keeps your devices in step. That is not the same as an archive. A route you delete is deleted everywhere.
Export anything you would be upset to lose. Select the routes and use File › Export Route to write GPX files you keep yourself. See exporting a route.
Tip: GPX is a plain, open format that any planner can read. An exported archive stays useful whatever you use later.