I can imagine that Rome's political class was well aware of the implications of Augustus' new powers. However, is this something that ordinary citizens would also have fully comprehended? Or would they have truly believed that Augustus was merely the "first citizen" as he claimed, and that Rome remained primarily a republic?
The key is that the transition was very, very incremental, over a long period, and at each stage Octavian's maneuvers were obfuscated behind a façade of "Republican" normalcy. See here for the background so I don't have to type it again. In essence, the "First Settlement" relied on established Republican precedent with some new twists. It was not exactly traditional for Octavian to hold the consulship every single year for 8 years, but nearly a hundred years earlier Gaius Marius had been consul seven times, so this was not completely out of left field. It was also not exactly traditional for Octavian to hold multi-year proconsular imperium over a single province, but this had already been done numerous times in the past: Caesar and Pompey both held provinces for periods of 5 years in the 50s BCE, for instance. Now in 27 BCE Octavian took several provinces all at once, which was new but again not totally out of left field.
Even when Octavian put down the yearly consulship and (eventually) got imperium proconsulare maius, the concept was not completely unknown. Pompey, as I mention in that older post, had imperium maius as part of his special powers package back in 67 BCE against the pirates, and he wasn't even the first benefactor of such a package. A guy named Antonius had received something nearly identical decades earlier. And the ancient Republican office of dictator had a similar concept.
Really the most radical move of Octavian's transition was the permanent tribunicia potestas, or power of a Tribune of the Plebs. This was very against tradition but no one balked or blinked (at least not visibly).
I've written it many times before on this sub, but really Augustus' greatest accomplishment and the real key to the transition to a hereditary authoritarian governmental system was the fact that he lived so damned long. It was 45 years between Actium in 31 BCE and the death of Augustus in 14 CE. That is a very very very long time in terms of politics, and by the time he died, there was no one left alive who could even recall what a "normal" Republic should be like. The Republic had not been "normal" since the 60s BCE (and even then, questionably). There were 73 years between Caesar's contentious consulship in 59 BCE and the death of Augustus in 14 CE, and that's 3+ generations.
This answer by u/TWG26 may be of use to you