A conditional formatting formula like below will check is the week number of a date entered in A1 is less than the current week number minus 1 or on a particular date. In the formula I hard-coded September 1, 2022, but you could replace that by a reference to a cell that contains "a specific date".
=OR(ISOWEEKNUM(A1)<ISOWEEKNUM(TODAY())-1,DATE(2022,9,1))
In Excel for the web, it looks like this:
