The distance from the sun to Pluto is about 5.9 billion km. The radius of the sun is about 696,340 km. The ratio of radii is about 8,473. Cube that to get the ratio of volumes, and you get 608,263,848,559 for the ratio of volume in a sphere out to Pluto vs volume of the sun.

(Doing the numbers, I'm actually surprised: I had expected the ratio of radii to be bigger than 8,473. But I'm not surprised that the sun barely takes up any space.)

Arguably, the entire heliosphere is part of the Sun's atmosphere, and it reaches well beyond Pluto. If I were in a relativistic spaceship, I think I'd want to apply the brakes well before slamming into the heliosphere.

What do you call the heliosphere of a star that isn't the Sun? The stellosphere?

"Stellosphere" is wrong, because "stella" is Latin, and "sphere" is from Greek. It should be "asterosphere", but that's a word I've never seen nor heard.