Get a Casio G-Shock. The 800 models can sync with your phone and the time is auto corrected. I bought a GBA-800 from a pawn broker - out of the dozen or so watches in my box it's the one I reach for if I have to know what time it is accurately.
The watch uses the WWVB signal for nightly syncing. However, living on the East Coast means syncing is very dependent on day-to-day atmospheric propagation. When I visit more inland, it works great.
The watch face is solar powered, so I’ve never had to change the battery.
It has since been retired after 8 years of use for an Apple Watch, but I think fondly of the mighty job it did.
Actually in the process of choosing a casio lineage (waveceptor movement, metal case, sapphire crystal) - do I get titanium or blacked out stainless steel, lol
My synced G-Shock is always correct to within better than one tenth of a second, that is, to the limit of observability. Solar powered, too, so it's just an utterly reliable black box. My favourite gadget by far.
NTP isn't nearly that inaccurate.