Most (all?) of the modern Battlefield games have some sort of suppression mechanic. In fact, it was so strong in Battlefield 3 and 4 that an LMG with a bipod could be enough to render a sniper several hundred meters away wholly ineffective as their scope would shake too much to land any sort of a shot, even if your LMG could barely land any hits.
I'm pretty sure Battlefield V also has suppression, it's just not as noticeable since most of the full auto weapons would never reach out far enough to suppress snipers (where the effect is most apparent).
Battlefield 2042 is a terrible game and I haven't played it since my first 3 matches, so I don't remember if it has suppression.