You wouldn't calculate the sonotube for axial only anymore. It would now be axial + bending moment, where the bending moment is eccentricity (say 2") times axial force. If it's reinforced sonotube (though I doubt it for such small diameter), it should still work.
Technically, the bearing pressure distribution will also change. Sonotubes work with skin friction and bearing pressure together (though I only design them for bearing pressure). You could use the skin friction to help with increased bearing pressure at one side. Though I'll be honest, I have no idea how to calculate this kind of thing. I'd look into manuals for eccentrically loaded drilled piers. If the stress in the sonotube is well below combined flexural/axial capacity, I'd use that as a sign post to determine whether complicated bearing pressure calculations are needed. With the rate I charge clients, at the point that I see that there's a problem, we're looking at reinforcement or post correction rather than doing like 4 hours of calculations. It is just a tiny sonotube after all.
I'd say let the numbers lead your decision about what to do. If it's failing by a small amount, you can work on optimizing the loading of the post (things like live load reduction). If it's off by a lot, you might have to start looking at reinforcing the sonotube or correcting the offset in the post, or adding another sonotube and post somewhere else to reduce the loading.
Deck foundations are quite prone to settlement and failure in my experience. I don't know why; maybe it's because they're so exposed to wind and rain. So I wouldn't just brush this off.
