I would love a round watch that uses an analog face but can still buzz me with notifications and do Apple Pay (or Google Pay). I’ve found ones that meet the first two but not the last one. I use my watch to pay way too much.
Skagen had these kinds of watches with their Hagen line. Ran on a standard battery for nearly half a month. You could set up notification groups so that the watch would buzz and the watch's hands point to a specific hour.
I researched what kind of battery it was: CR2016, some kind of Lithium battery.
And boy, what a brain fart: I meant half a year, so six months. It's been a few years since I used that watch regularly, but I was impressed with the endurance of that little battery.