[Keysh]

You don't need a simulation; you just need an understanding of Newtonian gravity, basic algebra and a bit of calculus, and some knowledge of stellar masses, velocities, and space densities. This is a standard part of the grad school curriculum (even the advanced undergrad level) in astronomy; here's an example with the math in some lecture notes from an undergrad course at Caltech (by George Djorgovski): https://sites.astro.caltech.edu/~george/ay20/Ay20-Lec15x.pdf

The mean time for the orbit of a star to be significantly randomized by weak, intermediate-distance interactions (e.g., the kind the Sun is experiencing now from neighboring stars) is the relaxation time, and for a star like the Sun it's of order several trillion years.

The mean time between strong gravitational interactions, where the gravity of a single nearby star significantly changes the orbit of a star (perhaps more like what you were imagining), is of order one quadrillion (10^15) years.

(Note that the numbers are for the density of the stars at the Sun's orbit; further out, where you start to get to the point where dark-matter effects really show up, the density is lower, and so these times would be even longer.)

Those are examples of "extremely rare" even on timescales of the age of the universe.

[Retric]

I appreciate that link, but Dynamic relaxation is a much larger impact on velocity than required to be significant here. It’s still large enough to probably make such interactions meaningless on these timescales but it’s close.