Like Bob I’ve never used a tumbler and have always polished everything on the bench polisher. A spot of soap in an ultrasonic won’t foam as it’s only vibrating gently.
Can’t understand why solder would be dislodged unless it hadn’t been done properly, that seems very strange. We all use different methods, toothbrush, brass brush. If the solder remains intact With them then an ultrasonic will be fine.

If you want the finish to be great overall then you would need to polish chain and component parts with the same compounds to get a uniform finish