The energy needed for life there would/could be powered by tidal heating by Jupiter or Saturn and chemically sustained...The tidal forces would remain even if the Sun vanished.

Sure. That's the theory. However, the basis of life on this planet is photosynthesis. Without that, this would be a dead world. That requires illumination (sun light, preferably). We are talking about an era when we don't have this lovely fusion reactor emitting broad-spectrum light at the center of our solar system.

Plus, we haven't discussed what happens during the death of the sun. Sorry about getting into the weeds here. Occupational hazard. :-)

The sun will expand into a red giant. It is believed it will be large enough to actually engulf the Earth, and possibly Mars. Jupiter will become super-heated because of the proximity of the new solar surface to the planet. It's atmosphere is primarily hydrogen. It won't burn (no oxygen), but we can expect Jupiter to transform significantly. Meanwhile, the icy moons of Jupiter will almost certainly shed their icy layers. No telling how much sublimation of those moons' water will occur.

Then the sun is expected to blow off it's outer layers (a nova, but NOT a supernova). That will be a solar wind on steroids...lots of radiation, blowing off of at least some of the atmospheres of the outer planets. This will not be a benign thing, and seeking refuge of one of the icy moons probably won't save us.

If we don't have some sci-fi tech like warp drive, our species will be doomed. Again, I can't predict future technology. We may very well have a way to move a lot of people vast distances in a relatively short time. We would have to find a suitable planet (class M, if you're into Star Trek). And then hope that its biology is somewhat compatible with ours, and preferably we wouldn't be displacing some native sentient species (though that isn't a technical problem, just an ethical one).