Is it possible to fix a "knob twist" bath plug without spares?
A coat hanger will usually retrieve it , the “stopper” is a hollow tube that slides up and down to block the flow. I have used a coat hanger to pull the assembly up through the overflow tube many times. You can remove the stopper until you get the correct piece or just use the hanger to pull it up and down until you get the right piece.  I would take the pieces to a specialty plumbing store they probably have parts to fix it.