On day 3 of the prologue (it's open day at school) and oh wow, there are a lot of cut-scenes where the game takes control away from you and makes you watch people talk. I found myself yelling "Let me play!" at the game at one point when it again took control away from me for more exposition.

It doesn't help that you have to wait for the dialog to scroll into view rather than being able to make it appear instantly, and sometimes the cut-scene itself takes its sweet time to play out, so most conversations take a long time to read through.

Is the prologue just particularly cut-scene / dialog heavy to set up the story or is this the way the whole game is?

There are lots of cutscenes but there are lots of gameplay parts in the latter chapters. Prologue is very story heavy.