Everything you say is correct up until the last sentence. Metal-poor stars tend to be old, because the metallicity of galaxies is increasing with time (as fusion in stars and supernovae combines light elements into heavier elements).
Young relative to their own lifetime, old relative to us.
I meant young as maxnoe suggests but you’re right obviously, a better less ambiguous thing to say is that they are from a time/place when/where no other stars have yet had the opportunity to die.
Wait. That's an interesting statement. "Had" is the keyword which implies dual realities.
Guess a better way to phrase it is that metal-poor stars were formed long ago, relatively early after the big bang. If they're old or young depends on where in their lifecycle we observe them.