Oh, how oft have I wondered about these.
The coasters that go with the Bodum cups are a real puzzle. They absolutely look like they would have been made by Bodum to match the set, but those sets came with cork coasters so far as I know, not plastic.
There were cups like the below that had a sort of built-in plastic coaster, but that’s as close as I’ve seen—and it isn’t very close.
I believe the glass coasters are the same cocktail party plates from which Geordi munches white dragées in “Starship Mine.”
I’ve also tried to figure out what Troi’s teapot is, but never quite matched it precisely (it has an unusually large pouring spout but in other respects is similar to pots made by Parisian tea salon Mariage Frères).
So, in short (as usual), I share your curiosity, but have little in the way of answers. =\