Am I right that glide range will be unaffected by a higher density altitude but that time in the air will be shorter ?
Yes and yes.
Best L/D ratio is obtained at a particular angle of attack. It does not depend on air density.
At higher density altitude you will have to fly faster to maintain lift at the best L/D angle of attack, thus sink rate will increase, while glide range will not.
(But note that only the
true airspeed will increase. The
indicated airspeed will stay the same.)