ok, this says it all:
https://info.hdhomerun.com/info/app:fire_tv

Just updated to the FireTV Select, getting a No HDHomerun Tuners found

Can run HDHomerun on my Mac

Rebooted the HDHomerun,
Rebooted the FireTV
Remove the HDHomerun app, rebooted firetv and reinstalled.

FireTV HD Homerun:
Version: 20260820
for both the app on the firetv, and the Tuner

Tuner ...