Yes, far more. You have to actively generate tension in your posterior chain yo pull your body forward and up. Even to lean back into a bridge without falling you have to generate enough tension to counteract the force that would otherwise cause you to fall. If it were all about mobility then more people who could do a full bridge would be doing stand to stand bridges. Incidentally, it sort of does feel similar to a shrimp squat, but ultimately you have a lot more leverage in a shrimp squat because, even though you’re on one leg, your hips are not fully extended (as in the stand to stand bridge), which means more of your weight is forward by default. As a calisthenics athlete, probably the best 3 exercises for the lower body that one could do would be pistol squats, sprinting, and stand to stand bridges (or an even more advanced bridge variation). Barring the stand to stand bridge, shrimp squats and/or single leg deadlifts would complement pistols and sprinting nicely. Heck even “just” pistols and sprinting would be great, that’s more than I regularly do for my lower body.