I don't think the playing out from the back necessarily means possession play. I think he uses that as a basis for finding the space for midfielders to spring attacks from deep, especially against teams with a high line. When I watch the position of our players vs the position of City players, there is a stark difference. They always have 2 or 3 passes on, even in deeper areas, whereas we push our midfielders and attackers really high up the pitch and try to pick one of them out, which is where it falls apart a lot for us, in my opinion. I remember the same watching his Ajax team, quick passes between the lines and get from front to back as quickly as possible. Perhaps I'll have a read of what you posted as I had a limited sample size from games I watched, but I definitely don't see Guardiola-esque football on the horizon for us.
EDIT: I just looked up stats for both legs of Ajax vs Real Madrid and Ajax vs Tottenham in 2019. In three ties, they were outpossessed quite a bit, including the 4-1 win over Real. To win 4-1 with inferior possession tells you something, which is exactly what we are seeing now. They edged the possession 51-49% in one game vs Madrid.