I think Pep's being smart with this one, personally. Yaya finished last season with two pretty serious knee injuries that completely fucked him up and left him wincing after that 4-0 home win vs. Stoke. He's had a summer to himself to recover but Pep knows he can't be rushed back in just yet, not when Fernandinho, Silva and Delph are in such good form from pre-season.
Yaya will see out his contract, which ends next summer, and then he'll probably go off to New York to finish his playing days. If anyone can bring Yaya down a peg or two and just tell him straight that his best days or behind him and that he needs to take a squad role to prolong his physical condition, it's Pep - and that's if Yaya doesn't already know that himself.
They both get on, so if he does leave it won't be down to their relationship. Yaya was just a victim of circumstance when Pep took over at Barcelona: he was a utility player in defensive midfield who occasionally dropped into central defence, while the far more technically astute Busquets was emerging from Barcelona's B team. There wasn't really any way forward for him in Spain.
But during his time at City he's completely transformed his game. He's spent five years dominating entire seasons (yes, seasons) with his passing range and physical presence, he can move forward when asked, drop deeper when required, score goals of all types from anywhere on the pitch. His all-round game is miles better than it was when he left Barcelona and Pep will be fully aware of that.
Yaya can't perform the role he used to do so well anymore - he's only a couple of years from complete retirement and his legs are clearly feeling that fact - but he still has the vision, technical ability and awareness to make a good deep-lying playmaker, which is where Pep is likely to use him when Gundogan needs a rest or if we don't decide to pull Sagna and Clichy in-field.
He's just using him sparingly so we can get the best out of him in league games - we have a big squad and Yaya is no longer one of our absolute best players who can be depended on every week (like De Bruyne, Aguero, etc.) so we just have to use him carefully to get the best out of him. Dropping him for the Steau game while he gets his fitness back up is just sensible planning.