The Pi-hole team does neither develop nor endorse apps for Umbrel's app store, and Umbrel OS isn't on Pi-hole's list of supported OSs .
So far, we've only received reports for failing installs on Umbrel, see e.g. Pi-Hole in the Getumbrel node does not install, it always stays on.
It seems your installation succeeded, but your debug log is inconclusive, probably due to lack of proper permissions, which potentially could affect Pi-hole's operation as well.
But that is just me guessing - I wouldn't have a clue how the Umbrel app developers went about wrapping code around Pi-hole to offer it as an app in their store.
I'd recommend to file a bug report with the developers of that Umbrel App.
Are you just running Pi-hole on Umbrel?
Umbrel's FAQ reads:
That would seem an overly excessive h/w requirement for running just Pi-hole.
Pi-hole is designed to run even on low end, limited hardware, e.g. even a 2015 RPi Zero with a network dongle is fully sufficient of providing DNS services for your netwok.
So if you'd just want Pi-hole, you could consider a leaner server OS to run it.
On any RPi, Raspberry Pi OS Lite usually is a good fit.