You can use the boost feature. Your boosts are public, but that's usually a good thing. Things you want to save are often things you want to promote, and vice versa.
You can pull up a feed of the threads that you've upvoted/favorited in the sort method next to your username on the top right. If you change the view to microblogs, it also changes the feed to microblogs that you've favorited. It's a bit different from saving from Reddit/Lemmy, as I don't think there's a way to display saved comments yet, but I hope this will help a bit at least.