Most airlines don’t have a specific policy on visual or manual flying, aside from a recommendation of a latest time to engage the AP.
As with all airlines, it’s the Captain’s call and if he hasn’t briefed it correctly, complied with SOPs and made any poor decisions, he’ll be held accountable.
With this in mind, I wouldn’t be applying to any major airline hoping for lots of manual flying. Try the smaller wet-lease specialists, where perhaps things may be a little less restrictive.