Cranking issue with rough idle?

The car acted like it had a drained battery. Checked the positive terminal it was loose, terminal wouldn’t tighten, so I replaced terminal. Battery won’t hold a charge so get it tested and warrantied. With new battery still wouldn’t start, still sounding like low battery. Have 12.5v stable when off 11.5v cranking. Assumed starter even though it was only 4 months old, hoped for it to be a relay. Changed relay and turned key, now oil light was on so topped off oil. Held it to crank still sluggish, engine hooks, and idles super low (500 vs usual 900 RPMs) then shuts off. Crank again still sounding sluggish but hooks a little sooner, now it’s an erratic idle bouncing from 1,200 to 700, shuts off again. Try third time still sluggish start with gas now only slightly idles rough (1,100-800). Spray some carb starter in the throttle body while giving it slight gas and it cleans out and starts normal/idles smooth. What’s causing this?