"The Southern" solved this decades ago. Elecrostars from introduction had near perfect display screen and audio announcements.
"Travel in the front x coaches for Blah, Blah, Blah. This is coach number y of z."
To this day it's only the southern region TOCs who do SDO and splitting trains well, everywhere else is rubbish at it.
In the pre-Covid timetable there was a Down London Midland train in the evening peak formed of 3 x 350s. At Northampton the front 4 went on to Birmingham and the rear 4 returned to Euston, The middle four, after the others had left, went to the depot.
In each set both the automatic announcements and the interior and exterior displays correctly showed the particular destination for each different set - obviously the rear set showing Northampton, as well as the middle set. .There were also automatic announcements that 'the front four coaches are for Birmingham New Street' On arrival at Northampton there was the announcement 'this train terminates here' in the rear two sets. Usually the conductor made an announcement as well. I regularly travelled on it from Milton Keynes to Northampton and I usually tried to advise nearby people in the rear 8 cars that I noticed were making no attempt to move to move to the front 4 coaches. When I did so there were three responses; gratitude; indifference; and contradiction - sometimes hostile. The first category was probably the smallest but I regarded it as an experiment in human behaviour. If the train was late the last set could start its journey back to Euston quite promptly which I think may have caught people out, but the station staff did try.
Splitting and joining is still reasonably slick at Northampton. Not now for different destinations, just adding/removing sets 4 > 8, 8 > 12 and vice versa. All done by the traincrew of course.
In the halcyon days of the Sunny South Express through carriages from the East and West Midlands and the North East and East Midlands were reformed into two trains for different destinations on the South Coast at Northampton. I have a copy of the Carriage Working book - it was very complicated, particularly as the railway company providing some of the stock alternated between days. So nothing new up here either!