Rant: the 'new' brake caliper was actually a reman nightmare
So I grab a 'rebuilt' caliper for a 2004 Corolla at a place near Fresno, pay $85, slap it on. Brakes still drag after 2 hours of bleeding and messing with the proportioning valve. Turns out the piston was pitted under the boot, reman quality is trash now. Anyone else getting bad cores from these big chain stores or is it just my luck? I lost a whole Saturday on this.
That pitted piston under the boot is the tell right there, most remans just get a quick hone and a new seal slapped on so the pits stay hidden until the seal starts weeping. Next time you buy one, pull the piston out before you install it and run your fingernail across the bore, if it catches on anything take it straight back. The chain stores get cores from who knows where and the rebuilders cut corners on the plating, that's why yours dragged even after you bled it right. Also check the slide pins and the bracket ears, bent ears from a wrecked donor car will make it drag no matter how clean the piston is. For 85 bucks you were already close to a brand new one from RockAuto, which for a 2004 Corolla is cheap enough that I quit messing with remans years ago. Return that thing and get your Saturday back.