There's no reason for you to feel like your learning efforts are in vain. Backbone is indeed pretty old, but the ideas behind it are still very solid.
The issues that were addressed initially with Backbone were mainly - “Get your truth out of the DOM”. Because back in the spaghetti/jQuery days, that was the real problem. The idea of managing the truth/data/state properly still applies. Learning this is important.
Another important thing to realise is that Vue and React handle only the view layer. Backbone is a framework to handle Views, Controllers, Collections, Models, Routers, Templates (with Underscore if you will) and talking to anything RESTful. So, learning that separation of concerns is important. Views do some things, Controllers another, Collections and Models another etc. With BB you get to grips with what it means to think in Events (React would say Actions) and if you keep true to how you handle that - your codebase will be beautiful. You would need to learn this no matter what library or framework the buzzing developer community on the web believes to be hip these days.
Backbone has it's very strong companion Marionette, with a vibrant and active community (some 3k users on gitter if I remember correctly) that makes a lot of great decisions for you to nudge you on the right path, if you're building a web UI.
I believe you would only learn good and sane ideas about front-end development if you delve deeper into BB.
I recently read this interesting experience about going from React => Backbone. blog.cloudboost.io/reactbone-lessons-from-react-j…
Personally I am working with React at the moment and I've learned a lot of great things that will enable me to improve my Backbone code more as well. This is another thing about Backbone, you can mess it all up badly, or you can know what you're doing and end up with a great product, it's very un-opinionated.
You are not wasting your time learning Backbone and many large companies are building stuff with it. You would also do well learning Angular, Vue or React etc. No matter what lib you are busy working with, you'll need to learn the same things - managing state, handling view updates, declarative/imperative views, inheritance, events/actions, REST.
My advice would be to continue with Backbone until you're not confused any more. Until you understand what it's trying to help you with. After that you can decide that it's either something to continue with or that it's better to learn Vue.