One of today's lucky ten thousand. Most galaxies have a black hole at the center that mass at least a hundred thousand times more than our sun: https://en.wikipedia.org/wiki/Supermassive_black_hole
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)
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.