I agree that Solas wants to save what the Elves were but I fail to see how he will accomplish this without modern Elves. It is possible that there are other enclaves of Ancient Elves hidden from the world but that is a big if. On what Solas means when he says "The People" again he is clearly referring to Elves in general. His own words strongly suggest such and he has referred to the Dalish Inquisitor, Sera, and modern Elves as "his" people multiple times.
"I'd hoped, well, our people can sometimes feel the rhythm of the language despite lacking the vocabulary." - Solas to Sera
"The Humans have not raised one of Our People so high for Ages beyond counting." - Solas to Dalish Inquisitor
Regarding Sera, he more or less gave up on her because he feels that she doesn't understand him or the culture.
Sera: Don't you start.
Solas: I am reasonably certain I said nothing.
Sera: Don't have to. You're all fluttery from that Mythal place.
Sera: "Oh, Tevinter took our stuff," except turns out, elves did it themselves. Ppbth!
Solas: You cannot upset me wth what we found there.
Sera: Oh? Why's that?
Solas: Because, Sera, my genuine sorrow for the tragedy of our history cannot be diminished by a single moment.
Solas: That you do not feel this, well, you have my envy... and pity.
Sera: Well, you just... Shut it!
"The People" Solas referred to are the Ancient Elves, not the modern elves.