I agree, the season had a tinge of classic Who to it, a bit as if Chibnall's earnest investment in the series came from childhood memories but his interest wavered as he grew. For instance, given his age he might have resurrected the three companions formula from the beginning of Davison's tenure. However, a meager ten episodes was downright too few to give everyone their due, and even the Doctor fell victim to it.
Looking back at how other modern doctors were introduced, I recall that both Tennant and Smith (both at the start of their careers, more or less) were given
big scenes and
big speeches to establish their presence (Eccleston and Capaldi were already well known). Poor Whittaker was upstaged by a companion's grandma and had an action scene in a construction yard that mostly reminded me of Tom Baker's demise scene. I have no problem with a Doctor with a somewhat more
primus inter pares, more "Round Table" approach, but as the main attraction they should have allowed her some more grandstanding, so to say?
I'll confess that I was a wee bit confused by some attitudes this Doctor had. You mentioned "Kerblam", and yes, the Doctor took charge there. But then she declared that the same AI that thought that the best way to call attention was murdering innocents (which by the way did not work, as simply sending a box to the Tardis did the trick) was working fine, and left it there at the end under promises of a reform in company policies. Until next time the AI wants to be heard. Also, no one in upper management had to deal with any responsibility in that. "Come with me/and you'll be/in a world of safety violations/my factory has no health regulations" [courtesy of Honest Trailers]
Meanwhile, only a few weeks earlier it was apparently wrong to shoot five rounds rapid at giant murderous vermin. Thirteen evidently thought her solution, i.e. lock them in a safe place and leave them to the notoriously painless fate of death by starvation, was the enlightened way to proceed. I was... baffled, to put it mildly.