I know watches and smartwatches are big in the swimming community, but personally, I STRONGLY advise against wearing one at all, ESPECIALLY in a competitive context.
Not only are they against the rules in competition, they’re a hazard in practice. You’ll be swimming fast, doing strokes with extended-arm recoveries like butterfly and backstroke, and in crowded circumstances often.
This isn’t a question about lane etiquette/circle swimming correctly; you WILL be hit by someone’s arm, and you WILL hit someone yourself during your time swimming. Whether it’s wrist on wrist, wrist on head, or something else, you can seriously hurt someone with a watch. Not to mention the watch itself is at risk of breaking.
I swam competitively for over 15 years, and at a decently high level. I’ve been cut several times by swimmers wearing watches, and if I ever got the chance to speak with them after the collision I always asked them to take the watch off when practicing.
All that being said, if there’s only two of you in a wide lane, it’s fine. It’s your judgment call, but I advise against it. Any half-decent pool will have a pace clock anyways, and you can get your own heart rate pretty easily.