There would for sure a transition period, otherwise it would be total chaos, not just at a personal level, but an industrial one. And I don’t doubt that somepeople will continue using inches and cups until the day they die.

As for the speed limit comment, that’s a almost a non-issue - practically every car on the road today either has a setting to switch from MPH to KMPH (for digital speedometers) or for analogue speedometers it will generally tend to show both. At that point you don’t need a frame of reference, just make the number on your dashboard <= the number on the sign. That’s it. Though as you say, it would almost certainly be a case of both units being on all the signs for a long while.

It wouldn’t even take a couple generations IMO. Maybe a decade or two for official stuff to move over. I have absolutely no doubt that plenty of stubborn people will completely refuse to move over to metric for their personal lives, but that’s fine tbh. No one cares in Billy over in Idaho wants to keep measuring his ingredients in tablespoons/cups/pints/etc or say it’s a 20 mile drive instead of a 30km one. As long as professionals can all rely on things being in metric in professional settings