iPhone and Apple Watch buzzing simultaneously for text messages

Not sure if it started right after the Watch OS update or a few days later, but lately my phone AND my watch are both buzzing at the same time and it’s too much. It used to work as advertised (phone buzzes when phone unlocked, watch buzzes if phone is locked). I haven’t changed any settings.

[Re-Titled by Moderator]

Original Title: Some time in the last week or two my iPhone and Apple Watch started both buzzing for texts