Edit: I was wrong! original post below:
> Battery-backed self-setting “atomic” clocks that get their updates via the cosmic ether have been a thing for years and get me most of the way there, but damned if I could find one with a red seven-segment display that I liked (maybe someone else’s search kung-fu is better than mine?)
I found this with ~5 minutes of searching. I think it meets your critera: https://www.amazon.com/Sharp-Digital-Alarm-AccuSet-Automatic...
(Regardless, cool project! I think yours still looks better than this one)
The clock you've linked is not an atomic clock. It has a pre-programmed clock with a battery keeping it going. If that battery dies, you still have to set the time manually.