Usually, local anesthetic (with IV sedation) breast enlargements are done over the muscle since it is a lot easier to numb the breast and difficult to numb the muscle which is vascular and down deep.
There will be struggles on your part, and your doctors, to numb, and relax the muscle just with shots of local anesthetic. Tumescent local anesthesia helps, but tumescent anestheisa doesn't diffuse well into the muscle.
Nerve blocks around the ribs help a lot, but the lung can be punctured with this technique. Even numbing the breast with a lot of needle injections risks a lung puncture and has some dangers. Muscle itself is hard to numb with local anesthetic injection.
General anesthesia has risks, but most plastic surgeons prefer the extra time and comfort to sculpt your breast to fit your new implants.
I think it is best to allow your surgeon freedom to do the best artistic work while you are asleep. This avoids pain from local anesthesia injections that can be insufficient or that wear off too quickly.