Will the sun explode?

[Anomalocaris]

The estimate I saw say earth will remain habitable to complex animals for much less than that.   Basically in 200 million years, a threshold will be crossed where, in order to further reduce green house effect to keep up with increasing output of the sun, so much CO2 has to be removed that plant photo synthesis will become increasingly difficult.

Basically we are screwed either way.  If we keep CO2 in the atmosphere, then in 200 million years the average global temperature will go up 15 degrees, and humans will literally cook without artificial air conditioning because over most of the planet surface the wet bulb temperature will exceed the human body temperature, leaving humans unable to cool off by fanning or sweating.   If we reduce CO2 to levels that will keep large part of planet survivable in terms of temperature, planets will stop being able to carry on with photosynthesis.

Whatever the time-frame, there is a lot that can be done about it. Star lifting is just one possibility. Gigantic solar shades are another. Altering Earth's orbit is another. Honestly, I think this is nothing but an academic exercise because even using your pessimistic example of 200K years, our civilization will either be dead by then or so advanced that this will be nothing more than a minor inconvenience.

The conventional thought that humans are bound to planets is just plain wrong. There is enough mass in a single planet the size of Earth to build rotating habitats with the land area of approximately a billion Earths. I'm used to thinking big but that number astounds even me.

Rotating habitats using artificial spin gravity can be built to pretty big sizes (>300 square miles) using just mundane materials like steel. Using advanced materials like carbon nanotubes, they can be built with the interior area equal to continents.

Unlike planets, rotating habitats can be moved fairly easily - especially if you are talking about doing it over galactic time. The truth is, even a massive planet like Earth can be moved over time. If you can accurately predict the solar output increase, you will know how much mass you need to alter its orbit slowly outbound. I don't think Earth's value will be anything more than nostalgia at that point but if we are still around, we'll have the ability to save it.

All these solutions are still approaches limited by our current conceptual proximity to our pre-tool making, pre-firing using origins, the reflect an overwhelming desire for the comfort of the familiar in our solutions, and attempts to somehow preserve or replicate through brute force some aspect of the environment and identity we evolved and taken shape in over several hundred of millions of years.

If we have several hundred million years in which to improve all aspects of technology, and biology, then I suspect we would have achieve total fusion of biology and technology, seamless integration of mind and computer, and between biological consciousness and artificial circuitry.  We would have totally forgotten any sentimental attachment to savanah, jungle, oceans, mountains, our biological bodies, or even such sense of self as having been bequeathed to us through our evolution.  I suspect we might move by simply uploading ourselves, perhaps all of us, onto Hardened microcircuitry and then transmit ourselves as signals to a receivers at a different location.