When (and where) did the measurement of time in a day change from being measured starting at dawn (and the night at dusk) to a system where the numbering starts in the middle of the day and night? Clearly the Romans did it, hence our use of am and pm - but were they the first?

It goes back to the Egyptians and the sundial. Noon is at the peak where the shadow is straight and usually most visible. The Egyptians considered this the middle of the day. They then worked out that midnight would be 12 hours prior to noon and made it the beginning of the day.

BTW, the Roman, and for that matter Egyptian, hour length changed with the season. So all 12 "hours" of day were when it was light. Winter months would have shorter daylight hours and longer nighttime hours. There were no time zones. Everything was based on the sun.

https://www.vermontpublic.org/programs/2019-01-18/why-do-days-start-at-12-oclock

https://en.m.wikipedia.org/wiki/12-hour_clock

It remains difficult to prove, but is seems that the Romans did indeed institute the convention of the day starting at midnight.

The concept of dividing the day into 24 hours dates back to ancient civilizations. The use of midnight as the starting point can be traced to the Roman Empire. The Romans divided the day into two parts: ante meridiem (before midday) and post meridiem (after midday). The system of beginning the day at midnight gradually gained popularity and has been adopted and standardized by various cultures and societies.

https://www.ncesc.com/geographic-faq/why-does-the-day-start-at-midnight/

With only one minor modification - the substitution of the day of the Lord, for the day of the Sun [-] it has in most countries of Latin speech survived both the decadence of the astrologers and the triumph of Christianity. Finally each day of the seven was divided into twenty-four hours which were reckoned to begin, not as with the Babylonians, at sunrise, nor, as among the Greeks, at sunset, but as but as is still the case with us, at midnight.

https://www.beaglesoft.com/timehistoryroman.htm
Exactly who decided that days start at midnight, and when and where that decision was made remains,to me at least, so far, obscure.