Conditional Labeling based on First day of the Month

I have a list of dates and based on the factor of first day of the month, I need to label them. For example if Today is 6/1/2023 (first day of the month) the dates before 5/1/2023 should be labeled as previous months beause I still want to show May as current. Otherwise, if the date is any other date for example 6/2/2023, then all dates before 6/1/2023 should be considered as previous months. Any idea what type of formulation would solve this? Thanks
Book1.xlsx (8.1 KB)

How about this?

LET cutoff_date = IF day({Today})=1 THEN monthstart({Today}-1) ELSE monthstart({Today})
IF [Date] < cutoff_date THEN "Previous" ELSE "Current"

prev-month.morph (3.7 KB)