Hey uniqueshort, this is the exact issue I ran into yesterday. While I read in many places that this is expected behaviour, it does seem to prevent the PiHole from ever being able to update itself. None of my apt commands would work.
First thing I did was to temporarily add the PiHole itself as a DNS server, just to get past the Temporary Failure error. I edited /etc/resolv.conf
sudo nano /etc/resolv.conf
I added nameserver 127.0.0.1 right about the .53 line and saved it out. That immediately allowed me to do apt updates. I read a few articles on how to fix it permanently. This one seemed to do it.
How To Set Permanent DNS Nameservers in Ubuntu
Once I did all of that, everything works.
Oh, and after I updated form 5.0 to 5.1.1, none of my graphs and some of the pages seemed all broken. I had to Ctrl+F5 each one of those pages and the force reload fixed every page.
Good luck, and let me know if you have any problems with any of this.