Hi @Massi - I think I may have something for you. I created an example using your sample data in DemoCentral. You can open the Analysis by clicking on the analysis icon in the left menu bar, and then can open the calculated fields to see how this is built.
https://democentral.learnquicksight.online/#Dashboard-TipsAndTricks-Calculation-Churn-across-months
I know this is just sample data, and only for one user, but I think it should work on your full dataset with many users.
Summary is two calcs, for last month and this month, which just returns the monthly_active value if the date matches the logic (last month is first day of last month through same day as parameter for last month, this month is first day of this month through the parameter date). Then we do two more calcs which do a maxOver of each field, grouped by User. Last calc is to compare the two maxOver calcs and return the appropriate category (Churn/Retained/New).
Hope this works for you!