However, the basis of life on this planet is photosynthesis. Without that, this would be a dead world.

Maybe. One theory is that life predated photosynthesis, and that the very earliest life forms derived their energy chemically from deep sea hydrothermal vents rather than from sunlight:

Wikipedia: Abiogenesis - Wikipedia

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.

Sure - but not for a very long time after the earth is uninhabitable.

AIUI, the habitable zone pushes out past the earth's orbit sometime in the next 1-2 billion years. That's when the sun's gradual increase in output burns off all surface water. Meanwhile, the sun won't evolve into a red giant until about 5-7 billion years. Prior to then, the habitable zone stays well short of Jupiter's orbit, and Europa will still be frozen. That's a massive amount of time when the Earth will be uninhabitable but Europa will still be more or less unchanged, with whatever water resources still protected from sublimation by the icy surface.

The red giant phase probably does mean the end of any Jovian habitable areas - but that's much further out than the end of the Earth.