I step on the proper tiles and hear the noise coming from the table room, but when I go there, the stairs are not revealed. Did I miss something?

Here's what you need to do (Major spoiler below):
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Go back to the table room. One of the dwarf statues against the wall in that room has an arm that you can manipulate. Click on the statue's outstretched arm and this will activate the mechanism that opens the stairs down to the next level.