In addition to what @Equivalent-Ambition said, there’s a small group of tasks you can do at the Appleseed Timber Company and the Central Union Railroad Camp (you can look them up for more information). As for actual side missions, there’s also the ones for the Downes family in Annesburg, as well as Charlotte Balfour north of there. I believe there are a few smaller events that only occur as Arthur, which mainly revolve around houses being built over time to make the game world feel more alive and evolving, but they’re very minor. There’s also the lady accepting donations close to the tailor in Saint Denis, though I’m not sure if the event is available after Chapter 4. Other than that, I can’t think of any other things off the top of my head that are exclusive to Arthur. Just remember to also do the money lending missions if you hadn’t already, and you should be fine.
