Liverpool play on the wings too often for Thiago to really make a difference. That's the main difference between Klopp and Pep. Klopp will take the available wing space more often to insist with a) crosses or b) quick combinations between wingers and fullbacks, while Guardiola will usually put more effort into trying to unlock teams centrally, with overloads and short passing schemes and patterns. Klopp's approach vs a team sitting deep is not as much in Thiago's wheelhouse as believed. It's based more on playing into the empty areas fast (which are 99% of the time the wide zones), with quick exchanges, more than on building superiority through slick passing and triangles, in the crowded central channels.
Thiago is a mixed bag so far at Liverpool because the team doesn't give him that much creative license. The approach insists more on Mane, Salah, and their corresponding fullbacks, Robertson and TAA.
In fact, the decline of Liverpool is tied to a drop in fullbacks' and wingers' level. Plus a collective drop in pressing intensity and duration (usually pressing is the first component that is lost in time, and this Liverpool team is in its 3rd season at the top).
