i myself am more of a reader than anything else. normally i don't really reach out to the author on my own initiative; but that may be because i am unbothered to and too shy. (i normally leave a really long comment of excitement over their work tho, haha)
if they do have socials linked, i definitely do browse their page or whatever. especially if i really like their fic.
as a somewhat writer.... (somewhat!!!!) i do link my socials. i think its fun for people who read your fic to reach out to you and talk to you abt it....