Isn’t the volume at the center of a large mass also larger?

I assume we have factored space curvature into our calculations for the behavior of stars and black holes, but I never see it talked about.

Can the same phenomenon be seen inside the sun? Does the estimate of when the Sun will expand into a red star account for this?

At the end of the article they say for sun it's 40,000 years.

Does this then portend that volcanic magma expelled has a younger half-life?

Not sure what you mean by volcanic magma half life but keep in mind the time dilation effect are minuscule, amounting to 2.5 years out of the 4.5 billion years of the earths age.