When Galadriel calls Sauron "him who holds the Seven and the Nine", I would say we're supposed to read that phrase as if she's giving him an ad-hoc title. She's not really claiming that Sauron literally has possession of 16 rings of power, because I can't imagine she would not know better.
Using the same quotes that @Matt Gutting uses, we can see Gandalf also speaks of "The Nine" and "The Seven" as if they were proper nouns
Seven the Dwarf-kings possessed, but three [Sauron] has recovered, and the others the dragons have consumed. ... So it is now: the Nine he has gathered to himself; the Seven also, or else they are destroyed.
(The Fellowship of the Ring, Book I, Chapter 2, "The Shadow of the Past")
Note that Gandalf does not say "the Nine he has gather to himself; and also what remains of the Seven", or anything like that. He says "the Nine [...]; the Seven also", before adding on the qualifier that some of them have been destroyed. He uses those terms as names for the set of rings given to men, and the set of rings given to dwarves.
Tolkien's use of capitalization is also a common literary technique to indicate that the word is more significant than its normal meaning would imply, and he's consistent about doing so:
The Nine the Nazgûl keep. The Seven are taken or destroyed.
(The Fellowship of the Ring, Book II, Chapter 2, "The Council of Elrond")
You saw the Eye of him that holds the Seven and the Nine
(The Fellowship of the Ring, Book II, Chapter 7: "The Mirror of Galadriel")
Taken as a whole, this seems to indicate that, among those who were "in the know" about the Rings of Power, they used the terms "the Seven" and "the Nine" to simply refer to the entire set, however many happened to still exist, of those rings. So, when she says Sauron is the holder of the Seven, she just means possesses all the remaining dwarf rings.