Yeah, that just doesn't gel with what I've been reading about them. Getting a different vibe from a sourcebook vs the original material isn't a good sign at all.
I have a few quotes:
"The Lyev Column enforces the law as Ravnica's police force" (p. 32).
Under why you might want to play a member of the Azorius Senate: "You're drawn to the idea of a hard-bitten police officer trying to impose order on a chaotic world" (p. 33).
"Most Azorius adventurers belong to the guild's police force. They are soldiers or spellcasters who patrol the city in teams or singly, preventing crimes or stopping them in progress. If you want to pursue a career in law enforcement, choose the path of the lawmage, the precognitive mage, or the arrester" (p. 33).
"Map 4.1 depicts an arrester station, which serves as the law enforcement hub for a precinct or neighborhood" (p. 129).
OTOH, the Wojek are only mentioned briefly:
"This special order serves as a combination of military police and military intelligence, giving it a fair degree of independence within the guild" (p. 43).
"Secondarily, the Wojek League is responsible for policing the ranks of the Legion" (p. 43).
From that, the Wojek in GGR are not what the vast majority of Ravnica would consider the police.