PHANGS-JWST: Data-processing Pipeline and First Full Public Data Release by Williams, TG, Lee, JC, Larson, KL, Leroy, AK, Sandstrom, K, Schinnerer, E, Thilker, DA, Belfiore, F, Egorov, OV, Rosolowsky, E, Sutter, J, DePasquale, J, Pagan, A, Berger, TA, Anand, GS, Barnes, AT, Bigiel, F, Boquien, M, Cao, Y, Chastenet, J, Chevance, M, Chown, R, Dale, DA, Deger, S