What is the final stage of the Sun's life?

The final stellar-remnant stage of the Sun's life is a white dwarf. In roughly five billion years, the Sun will exhaust the hydrogen fuel in its core and expand into a red giant, eventually shedding its outer layers into space.

The exposed core will remain extremely hot and dense, but it will no longer sustain ordinary nuclear fusion. This remnant, made mainly of carbon and oxygen, will be about Earth-sized while retaining a large fraction of the Sun's present mass. It will shine from stored heat rather than from ongoing core fusion.

The white dwarf will gradually cool and fade over immense spans of time. A hypothetical cooled remnant is called a black dwarf, but the universe is not old enough for any black dwarfs to exist, so white dwarf is the standard answer for the Sun's final known stage. The Sun will not become a neutron star or black hole because it lacks enough mass to undergo the collapse required to form either object.

The red giant phase is therefore an important late stage, but not the endpoint.