I'm running TVHeadend on a raspi4 using Docker no sweat. Records to an external HDD too which is NTFS formatted.
Whatever problem you're having here are with your setup. No one should be put off here with frights of 'incompatibilities'
The image I use is linuxserver/tvheadend but you need to change permissions on the DVB in order for docker to gain access. Pretty simple with a one line shell script.