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Geothermal heat provides less than 0.1% of the total heat of our planet. It is pretty much all just the sun. So as long as the output of the sun does not change much it won't be a problem (so will have to wait billions of years and even then sun will actually get bigger and hotter first before getting colder)

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The issue is that when the core cools too much it will cease to be magnetic, and then solar radiation strips the atmosphere.

But it’s not a major concern, in this case faster still means billion year time scales.

The planet is expected to still be mostly molten by the time the sun swallows it, so there is a huge margin. I think people underestimate just how much energy there is down there.

And it's being replenished by nuclear decay. It's not just the original heat from the compression/collisions of material when the planet formed.

Venus doesn’t have an internal magnetic field and has a thicker atmosphere than earth.

Won't Earth be engulfed in the first phase? If that's the case, Solar gasses will also drag down our orbital velocity and Earth will fall towards the core. So it won't be around for the second phase.

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