Nextcloud can easily handle 4Tb, I’ve seen guys with 50Tb instances with no issues
The backup problem is eternal. If you can, set up a consumer NAS somewhere else than where your server is and back up daily to it. Even over a slow connection, you should be able to get by after the first full backup.
If you can’t do that, either you go without backups and learn the hard way when your systems fail (I’m currently doing that, still waiting on the find out phase), or you will have to pay someone to store your data somewhere. From what I hear backblaze is affordable, but they do charge you per download. For 4 Tb, they would charge $180/year, with added costs per download which hopefully you can avoid.
A final alternative is to store cold backups somewhere else (at work, for example). Buy 2 external disks, and back up your server to one of them. Store it at work, then do the same with the other disk. Every month, rotate the disks. Your backup solution probably has a function to do exactly that, so you can leave one plugged in, accumulating this months data over time.