"... to the path." (The clarifying details are about the only thing that most people would like to see added.)

This assumes the clubs are fitted for you and that the groves on the club face are parallel to the ground at impact with the ball. If the groves are not parallel to the ground this too can create a side spin component to the ball;s rotational velocity vector, even if the club face is square to the linear velocity vector.
There's no Rule of Golf that says the grooves must be parallel to the sole (only to each other), so if slices could be counter-acted by angling the grooves, manufacturers would have been doing that for decades. Grooves don't matter in this regard.
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In addition unfitted clubs can cause the sole of the club to not impact the ground evenly (e.g. the toe or heel of the club might strike the ground first twisting the club into a closed or open position at impact. Clubs that are to upright for you causes to toe of the club to impact the ground first causing the slice I believe).
We impact the ball before we impact the ground, so any twisting that might occur after the ball's gone is irrelevant. A club that's too upright will lead to shots to the left for the same reason that if you swing a club level with your shoulders, the face points varying amounts left (depending on the club's loft). Vice versa for a club that's too flat.
















Mine was able to make the same swing after changing his clubface angle, yours needed extra swings.






