Highlight Month Columns based on dates in Google Sheet

I would highlight, in Google Sheet, the columns of months based on dates in col AA:
dd/mm/yyyy (start date) - dd/mm/yyyy (end date).

Example:
Col AA ---> 25/05/2022 - 06/09/2022
The columns that must be highlighted: from May to September.

Solution

You can try a much simpler formula:

=(EOMONTH(DATEVALUE("1/"&C$1);0)>$A2)*(DATEVALUE("1/"&C$1)<=$B2)

this works for current year.

If you want to use another year add it to string in DATEVALUE function, i.e. =DATEVALUE("1/"&C$1&"/2020")