First images from Euclid are in

Do the captured elements move a lot during this snapshot? since it will take months? Is the difference significant?

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.