In order for a route to be sync-d to the device, you must add the route to a collection. And that collection must be selected for sync-ing to the device. It is apparently no longer possible to sync the legacy "Library" itself.
At worst, with an existing collection, this is a multi-step process. It's slightly easier if you want to create a new collection.
To add a collection, go to the Map tab for your account at explore.garmin.com. In the left sidebar, near the bottom, you will see a header for Collections. Click the plus sign on the right of the header to add a collection. In the resulting fly-out, give the collection a name. If you've already imported the routes you want to sync into the Library, click on the Routes tab (the icon is the two connected push pins), and select the routes you want to add to the collection. When you've selected everything you want to add, click Next at the bottom right of the fly-out.
On the next page of the fly-out, you must select your iR device under the heading Sync This Collection to These Devices. You can optionally choose to show the collection on MapShare. Now click Save Collection in the lower right of the fly-out.
Sync and you should be good to go.
At any time, you can control which collections will sync to the device from the Plans & Devices tab of your account. Click the Collections button for the device. In the resulting pop-up, select (or de-select) the collections to be sync-d to the device. You can also control change the active collection from here. The active collection is the one to which activity on the device is added. Click Close when done.
If you hadn't yet imported the tracks, or if you want to add more routes later, it's easy to do even if the collection does not yet exist. When you import a new track as a route, you will have the opportunity to add the route to existing collections, add new collections and import the routes there (including the ability to specify which new collections sync to the device), or just import into the Library (meaning you will have to manage it later to get it onto the device). Just follow the directions in the import pop-up.