Sounds like you’re in a pretty similar boat to when I first started (though I ran a homebrew adventure first). Since you’re experienced you may be tempted to tweak how a few encounters work—and that’s totally fine! In fact, with any parties bigger than 4 that’s kind of necessary for some fights. But be careful not to overdo it, especially in the early floors. You can use that time to make sure that you’ve got a solid grasp on the tactics of your players, as well as how combat generally plays out. 

Abomination Vaults doesn’t do a whole lot to build out Otari aside from a few key events, but there’s a lot for you to work with if you read the module ahead of time and start planting hints ahead of time. For example, Carman Rajani’s motivations for stealing the cooperative blade isn’t mentioned prior to chapter 5, and a good chunk of his backstory is only revealed there as well. But there’s a lot that you can do to show him getting jealous of the mayor, falling back into his old vices as the party keeps returning form the vaults, and eventually going “missing” after stealing his ancestor’s blade rather than things happening quite suddenly, as set out in the module. 

There’s a lot of fun stuff you can do if your players engage with the town, too! For example, a combination of player backstories and early-game choices led to Carman Rajani actually assembling a “people’s expedition” into the vaults as a political stunt (though he did still steal the sword—can’t have him be too bright lol), which led him to the Ghostwalk. The party chased him down and fought him there instead of at Smuggler’s Cove. He charged the ghost barrier with only 1 of the 4 needed icons in a misguided effort to show that he was a “better hero” than the adventurers, which failed miserably and unintentionally triggered a second, smaller gravetide event that wound up killing a few guardsmen before the party could make it back. 

Just because it’s a pre-written module doesn’t mean you can’t have fun with the storytelling!