Here’s the thing with subdivision levels: in order for a model to have lower sub-d levels then it needs to be possible to actually create the topology of any higher level through subdivision in the first place.
For example, if you extract a 16x16 grid then it is possible to have lower subdivision levels because 16x16 is something that can be created by subdividing smaller grids. 16x16 can step down to 8x8, which can step down to 4x4, which can step down to 2x2, which can itelf step down to 1x1.
But if you grabbed an extra row and tried to extract 16x17 or 17x17, then you have a mesh with a topology that simply can not be created through a subdivision algorithm. Therefore that new topology can not have any lower levels; it has to be the base level.
So if you try to extract a mesh that already has subdivision levels and you want to keep those levels then you need to be absolutely precise with what you extract so that your final topology can actually be reconstructed through a subdivision algorithm. A single polygon plus or minus is all it takes to ruin this possibility. In addition to having a precise selection for the extraction, you also have to check over your extraction settings as these too can change the extracted topology (such as when it adds thickness).
Here’s the other kicker:
Even when you have an extracted subtool with topology that can be reconstructed, you still have to manually press the button to reconstruct the lower levels. The result shouldn’t have subdivision history automatically. I noticed your steps only mentioned clicking on the Extract button, but that button only gives you a preview. Did you click the smaller accept button afterwards?
(On a side note, “Alt + Shift + Ctrl” isn’t the same as masking. The Ctrl+Shift shortcuts are for selection/visibility).