It takes 230 million years for the Sun to make one full orbit around the Milky Way.
There are other (more probable) theories about the end of the universe, and if you’re up to it you can read more here: https://en.wikipedia.org/wiki/Ultimate_fate_of_the_universe
I’m in favor of the Big Chill, since I like the concept of entropy as introduced by the second law of thermodynamics: https://en.wikipedia.org/wiki/Heat_death_of_the_universe
The planets may be consumed, when the star runs out of fuel and swells a lot, and such is the Earth's fate. But that scenario is not one that happens to black holes.
The sun is 99.86% of the mass of solar system. So if you orbit the centre of mass of the solar system, you orbit the sun, more or less. Give or take a small correction for Jupiter.
But ... there are a lot more than a hundred thousand stars in the milky way. So if I guess right, the ratio of central mass vs the rest would be very different for the Milky way? It's more of a blob.
Even at "The current best estimate of its mass is 4.2 million solar masses" it does not dominate? https://en.wikipedia.org/wiki/Sagittarius_A*
(I think anyway, I just made it up, I'm not learned in this area, just a HN shitposter)
No. The Sun's orbit is determined by the total mass of stars, gas, and dark matter interior to the orbit. This is mostly due to the stars (we're not far enough out from the center for dark matter to be the dominant component) and is on the order of several tens of billions of solar masses.
(There is a supermassive black hole at the center of our galaxy, but its mass is only about 4 million solar masses, so it's negligibly small compared to the mass of all the stars.)
The Sun in turn orbits the the centre of mass of the Milky Way. But I don't think that the mass of the Milky way's central supermassive black hole dominates in the same way.