My only slight worry with Sane is that I don't want to see his development stunted and I don't want to see Raheem's development stunted. Pep doesn't really do "competition" in his squads, people generally tend to know their place. If we bring Sane in I hope it's so that both him and Raheem are our wide attackers and not so that one of them is constantly on the bench.
When people say Pep doesn't do competition, it's because he rotates so heavily that there's no 1st XI and subs - there's just the group of 16/17. The opposite of Mourinho, who has a really clearly defined XI and plays it every week.
At Bayern for example - Costa, Coman, Ribery and Robben. 99% of the time only 2 play, but they all play a lot.
You go back to the midfield in his first season - Lahm, Thiago, Schweingsteiger, Kroos, Gotze and sometimes Martinez as well, all competing for 3 midfield positions.
Balancing Sané, Sterling and Aubameyang really shouldn't be an issue for him. Sané can play left, right or striker, Sterling can play left, right or behind the striker, Aubameyang can play left, right or striker.
I imagine there'll be a constant rotation with 2 playing and one on the bench.