I like this concept quite a bit, once I got the hang of the mechanics I felt properly engaged the whole time. There's a steep learning curve to overcome, but I think it's worth it. Perhaps there could be a little more telegraphing on what an attack will do when it's queued? Like a target reticle for the projectile's target position, or the shield could have an initial pulse on each beat before it fully defends the player, for example.
Also, I think that even with the larger hitbox and understanding of the projectile attack, I was having quite a bit of trouble gauging whereabouts the square enemies were going to be. I think the constant, smooth movement makes them a bit hard to assess when making a snappy, 1-beat decision on where to shoot, and if I've made a mistake, it's far too late to course correct. Apologies for playing armchair designer, but I think the square enemies could benefit from moving in pulses as opposed to their current smooth movement, so it'd be easier to gauge their travel distance, and more time can be spent focusing on the rhythm mechanic, which I think is the meat of the idea here.
Nitpicks aside, this was still very fun.