I would suggest that you remove the 3-jaw chuck and use a dead center that has the same taper as your headstock (usually MT3 on mini-lathes). Similarly on the tailstock (usually MT2).? You've already shown that there is a misalignment with the chucks, but to adjust the tailstock, I would use dead centers that fir the tapers. Then adjust the tailstock accordingly.? Hopefully, the headstock spindle is aligned with the ways.
ralphie
Ralph Lehotsky