Way back when OTA TV channels were still analog, I modulated the output of my security DVR and combined it with the OTA antenna feed. That way, it was just a different channel to tune to, either via the Dish OTA tuner, or the TV's tuner.
After moving to the digital age, I have a network NVR now, and I use an app on a FireStick when I want to see the cameras on TV (rarely). Mostly I use the wall touch tablets used for my home automation, or my phone now.
What you want to do, can be done, but the cheapest HDMI to ATSC modulators that I have seen are close to $300 and don't have any builtin way to mix that into the same antenna input as the OTA channels. Of course, I haven't looked very hard for this as I have a solution that works better for me.