Sony cameras are fine for starscapes and Milky way photography.
The star eater issue can be a problem if doing astrophotography with a star tracker and good optics - images where objects in the night sky are of interest.
Later Sony cameras have a milder star eater issue (which actually is spatial filtering removing hot pixels, a very helpful feature in almost every respect - unless wanting to capture the faintest stars faithfully - the star eater issue does NOT affect brighter stars in the frame, only the very faintest ones).
Sony A7III and a tracked exposure: