that doesn’t require I keep a full local copy of all the data
If you don’t do that, the place that you call “backup” is the only place where it is stored - that is not a Backup. A backup is an additional place where it is stored, for the case when your primary storage gets destroyed.
It is not that easy to understand what you want, to me it reads like you want something like Nextcloud - i.e. your own little cloud, where you can put all your stuff, and view it through the webbrowser or the nextcloud apps, and also keep selected parts of your stuff in sync with your devices (or automatically upload photos take with your smartphone for example).
Backup of Nextcloud (or whatever you want to use) is a seperate topic. Any incremental backup tool would apply though, so there’s much to choose from. I personally use btrbk which uses Btrfs Send+Receive to push incremental snapshots to an offsite server.