Even that isn't going to necessarily help.

When the sun depletes all of the hydrogen in its core, gravity becomes the dominant force once again and it starts collapsing. Eventually, the temperature and pressure increase from that collapse will ignite helium fusion, but in the time between those two events, the core will have built up some amount of inertia, which means the collapse continues and overshoots the new equilibrium point. This means the temperature and pressure further increase, adding even more helium fusion to counteract it until the pressure generated from that fusion overcomes that inertia.

But this rebound will also be an overshoot, but this time pushing outwards, followed by a reduction in temp/pressure, reducing fusion, then another collapse once gravity overcomes that inertia, and it'll oscillate like that for some time.

The science isn't exactly certain about what specifically this will look like but I'd be surprised if it isn't "strip the atmosphere from the earth, even if it's already in the new goldilocks zone for once the sun eventually reaches equilibrium" levels of violence, possibly on each outward oscillation after that burst of higher fusion energy.

Oh, there's also still a huge amount of hydrogen in the outer layers that are collapsing with the core, suddenly being pushed on with the force of helium fusion, that can also ignite hydrogen fusion in the outer layers as it oscillates, adding even more energy, though this could act to dampen the oscillations, but it will still be violent in our direction.

My guess would be best case is humanity is forced to live underground for several million years, if we are able to tune energy gatherers properly to keep producing solar power but not get destroyed by those periodic mini novas.

Also, even if we can manage the heat from the increased radiation, the higher pressure solar winds might overcome our magnetic field during the new equilibrium anyways. There might not be a "goldilocks zone" at all, at least not for our planet, unless maybe we can supercharge our magnetic field, which might be possible since moving to another orbit is already a Type II civilization kind of thing (considering we can't just move our planet and expect everything to be fine with the rest of them, moving earth outwards will likely require doing something about the gas giants), so the rest of it might be trivial or solvable.

But it's fun and interesting to think about the details :).

True, if we somehow manage to not kill ourselves off it's possible we could change it or just leave the planet altogether.

As I said, that's if we don't do the job sooner.