Until a few weeks ago when a another TSA official berated me for thinking I could walk through a metal detector wearing a watch...
You're supposed to the watch/bracelet, but you do have to hold your wrist close to your body. You kind of want to hold your hands in front of your body as if you're about to grab one of your wrists with your other hand.
Watches and other jewelry are basically right at the cutoff of detection. They want to detect small knives but not earrings.
This is all absolutely tribal airport knowledge. I had been traveling for work for years, taken hundreds of flights, but I only found this out when my partner tried to go through a metal detector with a semi-permanent bracelet that requires a small screwdriver to take off, and the TSA person mercifully told her exactly how to pose as she walked through the detector.
Most recent flight we took, she couldn't find her passport for the extra security check right before the gate. It took us about half an hour to get around to having the security open up the (now closed) bag scanner, which lo and behold, had somehow eaten her (securely places in the bin) passport. The tech was shaking his head, saying "See, this is why you don't put your passport loose in the bin" as if that's a normal thing everyone already knows specifically to avoid.