I think I have a similar problem, I reported the problem as "speed brake" staying up on the right side. I also am using a TCA Sidestick and have tried several different settings. i.e. with Spad.Next, without, same MSFS 2020 hardware setting that I use on the Fenix A320 or just a "default" hardware setting for the Sidestick and I have the same problem. On the ground there is no indication, when I do the after start checklist all of the flight controls are normal. I only have the problem once I am airborne. finally, unlike the OP the aileron do effect my flight causing the AC to constantly turn to the right (roll).