Bernoulli's principle alone is not sufficient to explain the Magnus effect, as it doesn't account for the negative Magnus effect and lift/drag crisis that could happen under specific conditions. Flow separation, AKA boundary layer separation, that involves the boundary layer, point of separation, laminar-turbulent transition, wake, lift, drag, Reynolds number and spin parameter etc. is necessary to better explain the Magnus effect.
To keep it short, boundary layer is a thin layer of air that attaches to the surface of the ball in the direction of travel as the ball flies across the air. Depending on the spin, the boundary layer could separate at different points on the forward-moving and backward-moving sides and transition from laminar flow to turbulent flow, which is determined by the Reynolds number and spin parameter. The asymmetrical flow separation deflects the air and creates a pressure difference in the form of wake trailing behind the ball, generating an aerodynamic force that is comprised of lift and drag, in addition to the friction between the surface of the ball and the air.
Contrary to the results and predictions from wind tunnel tests, a few Japanese studies show that the negative Magnus effect that is common in some sports like football, volleyball, and baseball, where a spinning ball exihibits unpredictable behaviors in flight(e.g., a backspin ball curves down like how a topspin ball does), doesn't occur in free-flight tests of an actual table tennis ball launched with backspin from a customized 3-rotor robot within the range of speed and spin typically seen in table tennis. However, they find that there is a significant drop in the lift coefficient for some combinations of Reynolds number and spin parameter where the negative Magnus force is observed in wind tunnel and water channel tests. This "lift crisis" causes the lift force exerted on the ball to fluctuate widely due to the unsteady laminar-turbulent transition. A similar but less prominent trend is also observed for the drag coefficient.