Although the M1 mini certainly has plenty of power, I'd probably avoid that for now since they are so new and using it as a media server is a bit off the primary use case so IF you run into any issue, it might not be a quick fix if it needs something that is outside the developers here. But it is officially supported.
Personally, my use case isn't a huge bit different from yours. We have a couple of Apple TVs and a couple of Android TVs and also watch some on iOS. I'm running Channels DVR on an old 2012 Mac Mini that I had in the closet being unused. It was the cheapest model when it was originally bought... 2.5Ghz i5. The RAM was upgraded to 10GB for other reasons in the past, and main drive SSD. I have 3 x 10TB USB3 external drives dedicated to Channels DVR, and 2 x quad tuner HDHRs (total 8 tuners). For sources, I currently have OTA via an attic antenna, Philo, and Pluto... and sometimes we share a YoutTubeTV source that is my daughters. I have seen it doing 12 simultaneous recordings before, as well as processing recordings for commercial skip and serving up streams to the TVs. It seems to handle whatever is thrown at it without much of an issue. The Mini is also running Docker for Pluto and Plex, but Plex isn't used much.
I too used a Roamio as my last of many Tivos before jumping ship several years ago. One thing I'd caution you about with Channels is that if you are doing a lot of OTA recording, it doesn't handle tuner conflict as gracefully as a Tivo. If you run out of tuners with recordings, there is no quick and easy way to tell it to stop one of them so you can watch live TV if it runs out of tuners. You'd have to go into the recordings and manually stop something. That didn't pass the wife test for me so I just bought another HDHR to give me 8 tuners and never have that happen.
My setup runs very well most of the time. Occasionally I've had to reboot the Mini. It isn't often enough to spend the time trying to diagnose.
If I were starting off fresh with Channels right now, I'd probably look for a more recent Intel Mac Mini. Hard to beat for performance and very easy to work with. A NAS box may provide more disk redundancy, but the processors in them are usually pretty weak in comparison to a Mini, and they are a lot more expensive for the same compute power. I'm no that worried about spending a lot of money to avoid ever losing anything, but if that's important then something to consider. Of course you could also just use a RAID device as backup and still run it on a Mini.
The only other thing I'd mention is that my HDHRs are on the same switch with the Mini, but all the Apple TVs, Android TVs and iOS devices are on Wifi via an Orbi.