My concern is the mismatch between the timescale we communicate with people and the timescale of the trips (minutes or hours vs centuries). It would be such a massive transition during your trip that it is hard to adequately describe it.
In the past information had to travel by people or pigeon (some sort of physical movement). Realistically this is communication happening faster than travel does. Currently we have the inverse, where information is faster than travel. This should similarly happen in this FTL world because of Ansbiles and that you can not just send ships full of people FTL but information (and presumably more easily). So I think the only difference is that the travel time is scale. Right now there's nowhere it takes months to travel and we can communicate instantly. In this scenario we actually have a mixture of past and present. We can maintain near instant communication but maximal traveling distance is years instead of days.