I wonder if the historical format you might want to look at for "Chat" is letters? Definitely wordier segments, but it's at least the back and forth feel and we often have complete correspondence over long stretches from certain figures.

This would probably get easier towards the start of the 20th century ofc

Good point, informal letters might actually be a better source - AI chat is (usually) a written rather than spoken interaction after all! And we do have a lot transcribed collections of letters to train on, although they’re mostly from people who were famous or became famous, which certainly introduces some bias.