Barkley has been relatively underutilized his first two years, I'm 1000% sure Garrett will ride him like a horse to the tune of about 400 total touches and then likely go with heavy play-action off of it to shield Jones, because that's the simplest, most obvious answer to what sort of offense they should run.
With that said, he's proven that he's mostly stuck in his ways with the ability to implement only minor adjustments like RPO's. He's not going to reinvent himself like Reid in Kansas City and he sure as shit doesn't have the football mind to consistently break down defenses with slight adjustments/variations to his scheme like Shannahan.
So I'd imagine their offense will be better than it has been the last two years just because they'll have a more common-sense approach and lean more on Barkley, and with his touches going way up I'd expect him to have an All-Pro type year, and perhaps a career year after kind of being held back so far. Throw in some designed QB runs with Jones and some shots off play-action and they should be able to cobble together a half-decent offense just based on how special Barkley is. But at the end of the day their talent outside of Barkley is average at best and I'd be shocked if they won more than 6-7 games with an offense that is decent against average to bad defenses, but mostly folds against good or better defenses unless Barkley just goes off individually.
And then as the years march on the changes that Garrett will implement this season that start off new/fresh will become stale, he won't be able to come up with new ideas, at least not ones that make a significant difference, and unless their offensive talent improves drastically over the next 2 years I'd expect it to be a dumpster fire by year 3.
And by drastically I mean by year 3 they'll need about 4-5 Pro Bowlers on offense to avoid the inevitable rot of a Garrett-led offense.