I love watching video of activity on the solar surface because my brain has no intuition for the immense gravity and plasma dynamics at play. It's almost like getting a glimpse of a world with different laws of physics.
...of course the temperature and hydrogen composition make it pretty different :)
Being in orbit, I would sense weightlessness while being in the presences of an enormous gravitational field. Just as in orbit around earth: gravity is still there, you just can’t feel it.
Would I notice anything different when weightlessly orbiting something 300,000x more massive than earth?
Yes, due to tidal forces being stronger at one end of you than the other. You could use the formula given below but it looks like about a quarter of a newton.
One other thing: not sure you could "land on the surface" because it's all plasma. Flying through it might be interesting.
Yep, that's a word! https://en.wikipedia.org/wiki/Spaghettification