Is it necessary to strip all of the previous paint before repainting my indoor metal spiral staircase?
If the paint on it is well-bonded and not flaking off or rusty (but it's inside, so rusty is less of a problem, presumably) then simply scuffing to the point where the new paint can bond should be fine.
When the old paint is flaking off, then you really have to remove it, since part of it flaking off indicates that the rest of it is a dubious substrate for new paint. Consider that the bond of the new paint to the metal is the bond of the new paint to the old paint, and the bond of the old paint to the metal - so if the bond of the old paint to the metal is at all doubtful, it has to come all the way off. Your description indicates that this is not the case.