Does your router indicate that you have DS-Light? I think O2 provides each customer DS-Light until they ask for a real IPv4.
To your second question: In case of DS-Light you don't need a new IPv4 IP every 24h because your IP is not public facing.
PS: I don't be sure, but the Fritz Remote Apps use IPv6 to ensure that they also work with DS-Light.
I use immich and nextcloud for the clients (my wife and my parents know that I only take care about that data) and on the server side I use borgmatic which has a local repository on the second drive inside my nuc and a remote repository hosted by hetzner called "storage box" which supports borg native.
Yes the remote is out of my physical access, but borg is fully encrypted and for 4$/3.6€/month for 1TB I feel good.
Before I started with borg and hetzner I had a rsync based backup with an odroid hc1 hosted by my parents, but that doesn't feel safe. Due to slow network by my parents I had to sync my local backup instead of a second backup from the real data and the monitoring was also very bad.
From my point of view: You have no backup, if it is not automated and you have no monitoring.