It's accurate to within 100 light years. See https://starchild.gsfc.nasa.gov/docs/StarChild/questions/par....

"Accurate to within 100 light years" isn't really a meaningful statement. The page you linked to is a simplified explanation that says the method is only accurate enough to be used for stars within 100 light-years of Earth, which is approximately true. We have measurements of more distant stars, but they become increasingly inaccurate with distance.

To be more precise, the relative error of a parallax distance measurement is proportional to both the measurement error and the distance. For example, the Hipparcos mission measured parallax with an accuract of roughly 0.001 arc-seconds. That corresponds to a 0.1% error at a distance of 1pc (~3 ly), or 1% error at a distance of 10pc, or 10% error at a distance of 100pc, and so on.

Note also that the page you linked was written sometime around 2002; since then, more sensitive measurements have been done, e.g. https://arxiv.org/abs/1401.0484v1

The only star that matters in terms of bending light affecting the measurement of parallax is our own Sun, and that's taken into account with modern survey missions (such as Hipparcos and GAIA).