I dont know.
Your sytem is in a weird state using System-V instead of default systemd for Raspbian.
Also all distro's out of the box have the lo interface configured and yours doesnt.
So some customization is screwing things up for you.
You could for diagnosing assign an IP to the lo interface manually:
sudo ip address add 127.0.0.1/8 dev lo
Restart pihole-FTL:
pihole restartdns
And check again if listening now on port 4711 for the API:
I dont know what network manager (if any) is taking care of IP settings for your system so you could make above IP address assignment for the lo interface reboot persistent.
Thanks for your help. I see that pihole-FTL is now listening on port 4711, but the Web UI still shows "Lost Connection to API". Moreover, requests are slow even from curl on the Pi!
This may be your best approach to get back to a known good configuration. Before you do this, export your Pi-hole settings with the teleporter function, then you can restore them to the new install.