Spike Growth's AoE can include separate "grounds" on multiple levels
Technically, Spike Growth is limited to the "ground", rather than to a given "surface".
The ground in a 20-foot radius centered on a point...
So, on a technicality, the spell may actually be limited to "the surface of the planet". However, exactly what constitutes "ground" is up to DM fiat. This question suggests that the ground is any walkable surface, but that doesn’t really clarify anything, because that certainly includes walls and ceilings, depending on a relative plane of gravity or special ability, like Spider Climb.
It's feasible that, in an "underground" dungeon, each of the surfaces, especially the floor-like surfaces, might qualify as "ground".
Regardless, your intuition that the spell in not limited to a particular "ground" is correct. In your example, "... the top of stairs that descend 10 feet...", the spell would include ground in a 20ft radius from the point of origin, according to the Area of Effect rules--specifically Spheres.
A Sphere is an area of effect that extends in straight lines from a point of origin outward in all directions.
and
If all straight lines extending from the point of origin to a location in the area of effect are blocked, that location isn’t included in the area of effect. To block a line, an obstruction must provide Total Cover.
So long as you positioned the point of origin such that you could draw a straight line to each of the desired "grounds", the spell affects them. This would include each of the stairs, as well as any ground at the top of and the bottom of the flight of stairs, so long as it is within the volume of the sphere; the same goes for an inclined surface. No DM should prevent you from casing the spell e.g. on the slope of a hill, simply because it's an incline. You could not, however, affect ground on the opposite side of an obstacle. So, you couldn't affect the upper floor if the point of origin was blocked by the ceiling.
It's difficult to argue that ceilings and walls constitute "ground" in any natural linguistic sense. However, it would be reasonable for a DM to rule that certain walls or ceilings do qualify, especially insofar as they connect to ground--e.g., again in an "underground" dungeon, the ceiling and walls might constitute the "surface" of the planet.