Test thoroughly (it might be a day out), in E2:
Code:
=IF((MIN(Table13[@[End]:[End]],DATE(RIGHT(Table13[[#Headers],[Q2 2022]],4),MID(Table13[[#Headers],[Q2 2022]],2,1)*3+1,0))-MAX(Table13[@[Start]:[Start]],EDATE(DATE(RIGHT(Table13[[#Headers],[Q2 2022]],4),MID(Table13[[#Headers],[Q2 2022]],2,1)*3+1,0),-3)))>0,"x","")
copied down and across.
Most of the length of the formula is extracting real dates from the table headers. It could also be shorter if you're using Office365 - are you?