If you're looking for free info, the Player's Guide for Abomination Vaults has an Otari gazetteer. It is player-facing info, so it's missing a little bit of detail, but it has a rundown on the whole town!
Troubles In Otari doesn't introduce a huge amount of extra information about Otari, but there is a bit. Abomination Vaults has a lot more info, and details on basically all of the important players in town.
Some of it can be found on PathfinderWiki.
If you had to pick and choose, you should buy the first book of Abomination Vaults “Ruins of Gauntlight” I believe is the name; even if you ignore the adventure entirely. It gives you locations and all sorts of the NPCs in Otari.
As others have mentioned, Abomination Vaults will give you more info thanks to the Gazeteer. There you'll fine all of the locations, the NPC of interest, as well as the types of Earn Income the players can leverage and the associated skill.
I would highly also recommend this pay what you want resource found on Drive Thru RPG
The Abomination Vaults Expanded
It gives the NPCS and town a whole lot more detail. I used this along my own interpretations to give the town a lot more life than the beginner box, Troubles in Otari, and even Abomination Vaults gives these NPCs. v Definitely worth giving the creator compensation.
I haven't run either one as well (planning to start this fall with BB -> Troubles), but something easy to throw in are quests and bounties; one is specifically The Road From Otari, and some of the others could probably be worked in pretty easily. They take about an hour to run, so they won't fill up a whole session, but might be something you can incorporate to flesh out the town.
The PFS scenario Bandits of Immenwood also takes place between Otari and Absalom, it should take about 4 hours to run; it's balanced for levels 1-4, so it should fit anywhere in those two.
You could also look into Abomination Vaults, which takes place in and near Otari and maybe set up some hooks. There is overlap in levels between those two, but you might be able to set up some rumors or other minor events that allude to the other and then run AV after you finish this game.
The Player's Guide for Abomination Vaults includes a ton of information about the major players in Otari: https://downloads.paizo.com/AbominationVaults_PlayersGuide.pdf
That said, don't worry too much about contradicting the official lore. This is your game, and if something in the guide contradicts something you made up, just don't present it to your players, they will never be the wiser.
Take a look at the Roseguard section in the pdf though. That should give you an understanding for why this town exists, and informs some of the politics that are currently going on.
If you are planning to run Troubles in Otari later, you should be aware that it consists of three short adventures dealing with the lumber industry, the delivery service, and an abandoned fishing shack just outside of town. If you want to ease your players into these quests, you may want to introduce them earlier.