I've always seen Hatter as a romantic interest for Cupid, someone he would actively pursue beyond just physical intimacy or casual hookups.
While Stephen was a teen going through the secret conversion therapy program being hosted at Arkham at the time, they would punish him for rebelling openly or being unable to follow the program. He'd get tossed into the cells of various rogues for short periods (as would other boys) in some sort of utterly deranged, utterly nonsensical effort to "scare them straight". None of the staff doing the conversion therapy were actual licensed therapists of course, and they absolutely were not doctors. Just a bunch of dumb, religious-brained bully zealots who had no idea what they were doing (other than brutalizing young gay teens, ofc!)...and they paid Arkham a lot of money to do it.
Anyway! Stephen encountered Hatter often this way. Stephen didn't find him annoying, instead they bonded in a friendly way; Hatter was a younger man then and sort of took a protective stance with Stephen as a teen, teaching him classic literary tales but especially Carroll. Sort of like a weird mentorship! He also taught him about technology, about the whole Alice thing, too, why they all call him the Mad Hatter. Stephen found a love for reading and science and gets the first taste of the psychology of controlling others. To me personally it's like very cute platonic bonding, friendship, an interesting touchstone for what's to come later for Stephen.
After the whole Ivy thing, and being reborn as Cupid, and murdering his parents (i.e. once he has the club up and running), he encounters (or reaches out) to Jervis again as a young man, Jervis is probably early 30s or so by now. It gets weird and fun fast, Cupid becomes an Alice for him and the relationship kind of progresses on its own. Cupid isn't into exclusivity but Jervis is so it becomes a little fraught at times, but they make it work. I think Jervis is the only person Cupid could ever truly be in love with at the end of the day.
I like their cozy dynamic even though they're both pretty cracked. Also Hatter's a CUTIE and a long-time fave of mine.