Same problem here. TV hat work with tvHeadEnd when installed on its own, hifiBerry works when installed on its own. When the other is added (I have tried the hifiberry first, then the TV hat and the other way round) In either case the hifiberry either disappears from the audio menu, or is on the menu, but does not work. I have searched the internet and tried the suggested 'solutions; to no avail. Not reloaded tvHeadEnd if the audio failed, so I don't know if the TV hat would still work.
Using PI4, PI TV HAT, official PSU and hifiBerry DAC+.
Buster loaded from official image, and then updated to latest version, but no other changes to software except make it "headless" (/boot/config.txt). Also set VNC, SSH, I2C and SPI active in Configuration.-> Interfaces because, as I understand it, the TV hat uses SPI and the hifiBerry uses I2C.
I have used Kodi and Plex, but these make no difference (this is where the issues showed initially as I used the TV Hat first, then bought the hifiBerry).
So why the conflict? Any ideas out there?