Parallax shift from the spacecraft moving along its orbit isn't measurable past 16,000 light years. The Milky Way is about 100,000 light years in diameter, so for most of the stars in our galaxy, let alone extragalactic objects, there's no effect.

For closer objects this shift is useful, as it's the only way to directly measure the distance to a object: https://en.wikipedia.org/wiki/Parallax_in_astronomy Every other method for estimating distances to astronomical objects (standard candles, redshift, etc) are based on parallax measurements.