Can I play Single Strike Mustard if my Bench is full?
No, you cannot play the card. Since the Bench is full you cannot search your deck, and since you did not search your deck you do not get to draw 5 cards.
Source: TPCi Rules Team (2022-09-08)

Relevant cards

Note: All applicable cards may not be listed below.
SWSH5_134
SWSH5_134