[Baeocystin]

You're right, in terms of the sun's ultimate lifespan. Unfortunately for us, the Goldilocks Zone is very sensitive. To achieve full solar sterilization of the Earth only requires ~10% greater output from the sun, for example. And that will happen long before the sun leaves the main sequence.

To give you an idea of the timescales involved, at the very birth of the solar system, right after the Earth coalesced, solar output was approximately 70% of what it is today.

It's not quite as bad as it sounds- if there is technological, intelligent life on Earth a billion years from now, simple diffraction gratings at the Sun::Earth L1 point could stretch the remaining time for hundreds of millions of years. Not something we can currently achieve, but it is within the realm of possibility. Beyond that is pure speculation.

https://en.wikipedia.org/wiki/Space_sunshade