Even before Wilson the Steelers would have been looking to the Draft for a QBOTF. Pickett was their fall-back position as #1 QB if they failed. He wasn't valuable enough for them to tolerate his being a problem. They'll sign a non-threatening back-up to Wilson for now and see what happens in the Draft. His forthcoming contract amounts for $1.984M and $2.623M aren't high for a usable back-up, (unlike Zach Wilson), but the money is still fully guaranteed.
https://www.behindthesteelcurtain.com/2024/3/15/24102346/kenny-picketts-departure-was-needed-and-now-the-steelers-can-move-on-russell-wilson-mike-tomlin
https://www.behindthesteelcurtain.com/2024/3/15/24102346/kenny-picketts-departure-was-needed-and-now-the-steelers-can-move-on-russell-wilson-mike-tomlin