I finally figured out that yes, the periodic chirping noise coming from the basement is indeed because there's a battery in the fire detectors that's getting low.
This was true in my old house on Beeler, but in that case it was very easy to tell that there was a battery in the fire detector, because it wasn't connected to anything else.
In this house, the smoke detectors have some sort of crazy ethernet-like cable coming out one side and a power cable coming out the other. So I figured, in the absence of any apparent battery compartment, that the damn thing is powered off the AC, and that's that, and WHY THE FUCK WON'T IT STOP just barely audibly chirping at a frequency (about once every twenty seconds) just at the edge of my annoying-noise periodicity attention span. But no, it turns out it does have a battery, too, and you can only get to it by detaching the AC adapter connector thingy and then opening the secret compartment thusly revealed.
But I can stop swearing in capital letters now because I figured it out and I can have my peace and quiet back.