Boeing's control columns are mechanically linked, but given (iirc) 50 lbs of force, they will mechanically desynchronize. If memory serves, they will snap back into sync once the force is released. I don't recall there being an aural warning for this.
The issues with Airbus's approach are that (a) in high-stress environments, aural warnings are the first ones to be unconsciously ignored, and (b) you get no haptic feedback, either from the other pilot's side stick, or from the control surfaces (since modern Airbuses are FBW, though you could still do electronic feedback via an active side stick). There's some talk of Airbus moving to active side sticks in the future to mitigate this issue.
The issue with Boeing's approach is that in a high-stress, tunnel-visioned situation, you can't tell another pilot's input feedback apart from something like jammed flight controls, a runaway stabiliser, or any other trim or autopilot malfunction, to name a few. There's also some talk of Boeing moving to active side sticks in the future to mitigate this issue.
[0] https://aircrafttechnic.com/wp-content/uploads/2020/10/Ads%C4%B1z-4.png