So far I have been running this campaign on Steam through my laptop. Just wondering if I were to get a tablet, would there somehow be someway to access my campaign progress through using the app on the tablet?

There is no form of cloud save or cross platform compatibility. If you could possibly locate the actual save data and transfer it manually yourself then maybe. I don't know how though and I've never heard of someone else pulling it off.

Steam cloud saving works for me and I have loaded saves from my tablet onto the desktop. Other people have reported issues though so I don't know if my experience is unusual. There does appear to be some weirdness to it, but there's some weirdness with app saving regardless (is it every round, or every adventure, or what?)