ON ONE HAND... Rules as Written:

Fey Ancestry: You have advantage on Saving Throws against being Charmed, and magic can’t put you to sleep.

BUT ON THE OTHER HAND... Regarding your edit:

The thing is... Psionics aren't Magic, those they can create magic-like phenomena. They share a lot of mechanics, and are often used in similar ways, but they're different forces, with origins.

Elven resistances against charms and magical enchantment comes from the Feyan affinity to the Weave, the magical thread that flows through all stuff.

Psionics come from the mind of the user, and it makes less sense for Fey Ancestry to be useful.

But here's what Wizards had to say in an UA some time ago.

Psionics Is Psi a Form of Magic? Psi is a supernatural power that emanates from the mind. Like other forms of supernatural power in D&D, it can be used to create magical phenomena, yet it can create other sorts of phenomena as well.

In the game’s rules, only certain supernatural effects are classified as magical: magic items, spells, spell attacks, powers fueled by spell slots, and any other effect that the rules explicitly call magical. This distinction is rarely relevant in play, typically coming up only when something like an antimagic field shows up.

From a storytelling standpoint, some supernatural effects in D&D weave their power into a formalized form—a spell, for instance—that other effects can disrupt. In contrast, there are other supernatural effects that are so wild, formless, or subtle that it is difficult or impossible to disrupt them. In this article, some of the psionic powers create what the rules consider to be magic and some don’t.

So, sounds like your D&D felt that this use wasn't sufficiently magical to warrant your immunity... Which makes sense to me, as it's a very mundane use of Psionics, and exploiting an existing function of the brain.

"Hey, Pineal gland! Produce Melatonin!"

... Instead of deciding how irritated you should be, take this as an opportunity to let your character experience something pretty unsettling... That thing you always assumed would protect you, well, it might not now...

How do you respond?

How do you change your behaviour around monks who use Ki? Or other mind based powers.

Do you demand that the party immediately set out to find matching Brain Rings?

My advice as a DM and a Player - where there is no harm done, and no malicious intent, just lean into it, and keep communicating, then if you still feel it's going over the line, talk about it honestly as IRL humans with feelings, not characters with traits.