I've been saying the same but ten Hag's style is a hybrid of the direct vertical style which Rangnick likes to implement combined with possession play. But both Rangnick and ten Hag place emphasis on verticality.
But like I've said before, it wouldn't surprise me if Rangnick chose someone like Adi Hutter, Marco Rose etc, who would both be a natural choice as far as continuing on from the high line, high intensity, fast transition play style, with heavy emphasis on verticality between the lines, which is what I expect Rangnick to try to implement.
It also wouldn't surprise me if Rangnick got the permanent role on a 2 year contract, depending on how he performs in the next 6 months.