Notifications for likes and comments in shared albums (public synced collections) don't appear in LR 13.4 -- there are no yellow badges. And sorting by Last Comment Time doesn't work. (A previous report for the lack of badges in LR 13.3 and 13.3.1 is marked as Fixed.)
Here are the steps I took and screenshots of the results:
1. In LRC, I created a public synced collection "Test Sync" and added four photos to it.
2. In LR Web, I marked the second photo with a like and the third photo with a like and a comment (photos sorted by capture time).
3. After waiting for the sync to LRC complete, the likes and comment appear in the Comments panel. But there are no yellow badges and the thumbnails are not sorted by Last Comment Time (the second and third photos with likes and comment should sort first and second). View > View Options > Cell Icons > Thumbnail Badges is enabled, as demonstrated by the GPS badges on the thumbnails.
These screenshots provide all the evidence:
AdChoices