No, many mains connected clocks still use the power frequency for timing. As recently as four years ago we had the same problem: https://www.nationalgeographic.com/science/article/european-...
It's also interesting to look at Swiss railway clock homages. The design is iconic and quite readable, but the more interesting ones have what are marketed as "stop to go" movements that mimic the actual Swiss clock system. They tick as you would expect, but when the second hand reaches 12 o'clock, it pauses, and the minute hand advances one full minute. It's a strange effect, and then of course you start asking about what happens during that pause and how it was actually counting time around that dial (it would have to be a bit fast, wouldn't it?). From my limited understanding, this is because the system synchronized every minute at the top of the minute, and the system had been around since at least mid-century. Obviously it's just an amusement on a wall clock or wristwatch.