Based on that, seems like you want a security camera setup? Residential? Inside/outside? Budget? I don’t see anything about a smart home listed in your three bullets.
I run BI with HomeSeer. When I first installed BI with AI it worked really well. Alerts can be turned on or off based on what profile is currently running. But the profie would only change based on time of day. So I integrated HS so that when the garage door is activated or open, it would change the BI profile to no alerts. This was helpful to me as I would get alerts when my wife would pull into the garage.
Same for the back yard. If either one of us went into the back yard I would start getting alerts. Yes, you can manually change the profile, but that becomes a chore as we are in and out a lot. So I put a door sensor on the back door, wired it into HS, and now when the door is open I no longer get alerts from BI. We can go in and out all day and I don’t have to manually change anything. Its not perfect, but much better than getting alerts all day as we go about our business.
I like BI as I can run almost any brand of camera. If you go with a NVR you are typically forced to only run cameras from that manufacturer. Most NVR’s allow for a hard drive within them so no need for a NAS. Same for BI. Just use the hard drive in the computer.
Lastly, BI allows for the most configuration of any other setup I have seen. The ability to tune the system along with AI can get you to a point where false alerts are pretty rare. I ran a NVR system for 4 some odd years and almost every day i got false alerts. Eventually you just turn off the alerts and review the footage manually to see what happened. Got to be very annoying. Now with BI if I get an alert, I know it is something I need to pay attention to. Just what I thought a camera system was supposed to do!