That is what I have also read.
The Earth/Moon will be tidally locked long after the Sun is dead.
As for if the two will be engulfed by the dying Sun, that is still uncertain.
Whatever our decedents have evolved into, I am confident they’ll find a way to say themselves. Hopefully, by then, they will be spread across our galaxy. Still, the ones remaining might move all the planets away from the swelling Sun. Perhaps they will be wise in the ways of stellar engineering and be able to restart the Sun- one way would be if they could split all its atoms back to hydrogen and helium.