Add-on: same password, same identity.

That's not as far fetched as it sounds. Any website worth its salt will store your password as a hash, so if they started sharing the hashes with each other they could prevent you from reusing passwords without changing much security-wise

It would be better if you had a local tool telling you that - one that you control and only exists on your personal devices, kind of like secure messaging platforms such as Signal.

Another great later would be for all compromised passwords found in breaches to never be usable anywhere ever again, thus helping to thwart the most common form of breach we see today: credential stuffing.

Sorry you can't use *******

That wouldn't help that much