What was Augustus' political bias? Did his status as Princeps make him officially impartial in the Senate? I would have thought his relationship with Caesar would make him "Populares"
Ave!
That's simply not how Roman politics worked. Populares and optimates were not political parties, factions, or affiliations. The optimates in particular don't really exist--optimas, and the more common bonus is a rhetorical term that is applied to pretty much whomever you want to apply it to at the given moment. It carries a baggage of class rather than status, and even then one can be included in the boni without being in the senatorial class--Cicero includes the equites in the category all the time and in many of his speeches the plebs are included in the category, so that one wonders who exactly isn't considered one of the boni. That the optimates are not indicative of a political mindset becomes immediately obvious. Cicero condemned repeatedly the indecision and constant internecine bickering about trivial matters that so absorbed the nobiles, whom he famously called privately piscinarii, "fish-fanciers." Nor was popularis indicative of a political affiliation. A popularis was simply a politician who prioritized the power of the citizen assemblies over the political support of the senate. A politician could put on a popularis hat without having any previous record of populist actions, and could take it off again immediately--in fact this was the norm, even Cato did it during his tribunate. The popularis hat might even be worn in cases where the politician was trying to support something seemed decidedly unpopulist--Cicero depicted himself as a popularis when he shot down the Rullan agrarian bill (and as far as the urban poor was concerned he was probably acting in their interest--generally the rural plebs supported agrarian bills and the urban plebs opposed them and supported colonial foundations). Even Gaius Gracchus, supposedly one of the first populares, passed legislation weakening the powers of the tribunate and was quite staunchly aristocratic. Roman politics had no expectation that a politician stick to a consistent platform--the very idea of platforms would have been totally alien--and it had no expectation that a politician place himself in a "conservative" or "progressive" camp, provided that such terms would even make sense to a Roman (they probably wouldn't). For more on this see this thread, and probably this one.
Suffice to say that the inability to categorize Augustus meet the same difficulties. He was a Caesarian, but that means almost as little as calling him a popularis--Antony was also a Caesarian. Antony shows how difficult the label popularis is. Antony was frequently accused of being a rabble-rouser, most notably when he started the riots at Caesar's funeral. But during his proconsular governorship of Italy Antony famously opposed the demagogue Dolabella, nearly causing mass rioting in the city and forcing Caesar to return prematurely to fix things up--a decidedly un-populist move. If we expect populares to support "populist" legislation (which I think we've seen we should absolutely not) then both Caesar's dictatorship and Augustus' entire career are hard to place. Both reduced the distributions of public grain (and Augustus made them essentially hereditary, and the privilege of a particular sub-class), both apparently abolished voluntary associations like the collegia. Neither were popular in their treatment of Italian land--Caesar's decemvirate was notoriously unpopular (and in 59 he and Pompey were booed in the theater) and Octavian took most of the blame for the bloody land distributions of the proscriptions, which benefited neither the urban nor rural plebs, only the Caesarian veterans. Octavian, while holding tribunician power, essentially did away with the tribunate and eventually with free elections in general, though a pretense was made until after his death. But simultaneously Octavian and Caesar were said to employ the power of the citizen voting body, or in Octavian's case the army, over the aristocracy--in 59 Caesar ignored the senatorial review (not in itself a crime, but certainly looked down on, and traditionally an action that got one labeled a popularis) and took his agrarian bill directly to the assemblies. One should not look for consistent popularis or...whatever the opposite of that would be (optimate simply doesn't cut it) action in a politician, because with all but no examples there was never any consistent action of that sort, nor was there an expectation of it