Suggestions how to measure time passing in days using screenshots?

Not sure if this would help, but in Sims time I go by seasons, days, and years. The year I start playing is Year 1. So I write something like "4 Winter, Year 1" for the 4th day of Winter in Year 1.

I have to keep it short because I use it to title photos in-game, but maybe the same thing can be used for weeks and days?

I have a year count in my save, it's currently Y225. If I need adding season I would use Y225Wi05 for 5th days of Winter in year 225. I don't bother with weekdays, but that might be because I play rotationally and often stop for just one day in each house. Sounds like the file name will be the easier way for you to sort your images? Even if you edit the file name, yu might still be able to sort the files by date created, which might also be useful.