Your Gantt's chart is using MONDAYS as reference days, so your conditional formatting rule should make the same.
But the task are not always referenced to mondays, so first you need a formula so given any date it will return always the last monday of same week:
(Anydate-ABS(1-WEEKDAY(Anydate;2))
will return always a Monday. Now with this you can create a better CF rule:
=AND(($A6-ABS(1-WEEKDAY($A6;2)))<=C$4;($B6-ABS(1-WEEKDAY($B6;2)))>=C$4)
I'm using type 2 on WEEKDAY so Monday will be the first day of the week. Read documentation about it:
WEEKDAY
UPDATE: As suggested by @TomSharpe in comments, a different setup for Weekdate
could be used to make a shorter formula, using type=3.
=AND(($A6-WEEKDAY($A6;3))<=C$4;($B6-WEEKDAY($B6;3))>=C$4)