Did any of you have Joe Mode turned on?
I use Joe Mode in my Model 3, and today I noticed the turn signal clicking was a lot louder than usual. I went into settings and confirmed that Joe Mode was still toggled on. So I toggled it off and back on again, and that immediately quieted the turn signals. So it appeared to have been a software bug.
(I didn’t do a recent software update or anything like that that might’ve triggered a reset in the settings.)