Does the gravitational field change in the vicinity of a nova? Since gravity is calculated based on the product of the masses of two bodies and the distance separating them, I initially thought that the orbits of the outer planets would not be affected when our sun swells up to become a red giant.
But then I realized that I should not treat the sun and pluto as point masses. As the sun swells up, its mass (though unchanged) is distributed over a larger volume.
This cartoon
https://astronomy.com/magazine/ask-astro/2020/09/what-will-happen-to-the-planets-when-the-sun-becomes-a-red-giant
shows a larger sun that swells to the size of the Earth's orbit. Now in this setting, the distance , r , we use to calculate gravitational attraction will be much less.Would planets like Mars therefore orbit faster and and even closer to the sun?
Would we see more gravitational lensing of light when a star goes nova?
 A: If a massive body evolves without loosing any of its mass, so that its spherical symmetry remains intact, the gravity outside of it does not change. This is the consequence of the shell theorem .
However, as the Sun goes through its red giant phase, it will lose a significant portion of its mass (about one third overall) through the solar wind. As a consequence of such loss planetary orbits would expand so that $M_\odot(t) R_\text{orbit}(t)\approx\mathrm{Const} $. Also, for inner planets one should take into account tidal interactions and drag through greatly expanded Sun's chromosphere. As Wikipedia says (I added emphasizes):

For part of its red-giant life, the Sun will have a strong stellar wind that will carry away around 33% of its mass.[106][111][112] During these times, it is possible that Saturn's moon Titan could achieve surface temperatures necessary to support life.[113][114]


As the Sun expands, it will swallow the planets Mercury and Venus.[115] Earth's fate is less clear; although the Sun will envelop Earth's current orbit, the star's loss of mass (and thus weaker gravity) will cause the planets' orbits to move farther out.[106] If it were only for this, Venus and Earth would probably escape incineration,[111] but a 2008 study suggests that Earth will likely be swallowed up as a result of tidal interactions with the Sun's weakly bound outer envelope.[106]

A: When the Sun swells, its gravity will be as if coming from a point mass at its center. It will not change for Mars.
Gravitational force is the sum of forces generated by each part. The Sun still be spherically symmetric. While some points will be closer to Mars, some will be farther. The total will not change.
Deflection of starlight will be less because it is the deflection of a ray that skims the surface of the Sun. The surface will be farther away from the center, in a region where gravity is weaker.
