This idea of managers 'not handling pressure' is an overused trope. Unless its theorised how Arteta cracked under pressure, for example by bad tactical changes, it doesnt really mean anything. Most likely, Arsenal just fell apart due to having a worse less experienced squad, not because of Arteta.
By and large this idea of 'bottling' or 'imploded' is directly related to the strength of the squad. Better players handle pressure better.
City can 'handle the pressure' because they have the best team in the league. Just like how when Barca won all our titles we had insane squads, Madrid the same, City the same, Liverpool the same.
Not handling the pressure is 100% not a over used trope.
History is litered with managers who have stepped up and failed at the highest level.
The psychological aspect of the game is 100% real and what separates the greats from the very good.