One of Pep's most important attribute is he is sensitive towards the lads. This is major reason the lads listen to Pep.
If Pep wasn't sensitive towards them, then after a while the lads might have stopped listening to Pep. (It's happened in other big clubs won't mention their names).
New manager has to have senisitivity towards the lads. Else new manager could be one of best tactician coach in the world, the lads might well stop listening.
Also has to have experience of being in the hothouse a club setup where the top honours are played for. Pep had this in Barcelona A as player, in Barcelona B as coach.
Else when it comes to the crunch the manager will struggle.
I'm sorry to say nobody from Championship, nobody from outside top2 in the top leagues.
Playing style : the players have become accustomed to a style. To have a different philosophy from a a manager is jarring will show in negative results. So a similar variation to what the players are used to.
For me the manager that could fit all these : Ruben Amorim.