If my opponent has no benched Pokemon, does their Active Pokemon become Confused when I use Delcatty's "Captivating Tail" attack?
No. Confusion is only done to the "new Active Pokemon". If there is no switch, the Active Pokemon is not Confused.
Source: Darkness Ablaze FAQ (2020-07-31), TPCi Rules Team (2020-08-13)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH3_142
SWSH3_142