I think I've asked for this privately before, but this would be MASSIVE for me. Other apps I use/have used (right off the bat the self-care app Finch and your competitor Timelime - yes, ending in "lime" - come to mind, but I know they're not the only ones) allow you to set a custom time that your day officially starts (and thus is also the time the previous day ends - think of it as shifting midnight practically speaking).

Honestly, I've considered switching to Timelime for work AND personal (currently I use just the free version for personal only). Some of their differentiators are good, but they're really only nice-to-haves for me. I actually manually export the CSV files and change the dates of all the Sessions that occur before my bedtime, and this is a huge pain. This one single missing feature in Session really is THE number one feature that is most important to me in a productivity app.

As for Marcin's proposal, for me personally, I would need that time closer to 8am as I most often work overnight and consider it part of the previous day. So like Finch and Timelime, it would be amazing if you allowed the time of "day switch" or "new midnight" or whatever conveys the idea best, to be set to at minimum any of the 24 hours in a day. This way it can accommodate schedules of all kinds!