The (latest) Raspbian packages from the Cloudsmith repository are not compatible with ARMv6, hence Raspberry Pi 1 and Zero (1), anymore. Since "Raspbian" explicitly means ARMv6, I expect this to be a bug in the build scripts.
To replicate:
curl -sSf 'https://dl.cloudsmith.io/public/tvheadend/tvheadend/gpg.C6CC06BD69B430C6.key' | gpg --dearmor -o /etc/apt/trusted.gpg.d/tvheadend.gpg --yes
echo 'deb https://dl.cloudsmith.io/public/tvheadend/tvheadend/deb/raspbian bookworm main' > /etc/apt/sources.list.d/tvheadend.list
apt update
apt install tvheadend
tvheadend -v
You'll get an illegal instruction when executing the binary, and the service hence throws SIGILL, already while installing the package.
Doing the very same on an Odroid XU4 or any other Raspberry Pi model, works well, i.e. on ARMv7-capable systems, the packages have not an issue. There however one would use https://dl.cloudsmith.io/public/tvheadend/tvheadend/deb/debian
instead of deb/raspbian
.