Lilly Jay -- a clinical psychologist, and high school sweetheart of Broadway star Slater -- wrote an essay, published on The Cut Thursday, all about the public nature of her split.

In the essay, Lilly's lamenting she's now a spectacle in the public eye despite being in a profession where patients are better helped by not acknowledging their therapist's personal life.

She compares it to when she was pregnant with her healthy child while speaking to women whose own children faced life-threatening complications. Though she didn't hide her pregnant belly, none of her patients mentioned the pregnancy ... allowing for a detachment between the sessions and their outside reality.

Jay writes this split with Slater is much of the same ... with patients not acknowledging her very public divorce -- though she's constantly dragged into grief when seeing an unending promotion for "Wicked" -- Slater met Grande during the movie's production.

Worth noting ... she never name-checks Ariana specifically -- and, she doesn't attack her or her own ex-husband. In fact, she's complimentary of Slater, noting their romantic relationship is over but commending him on his 100% commitment to parenting their son.

That said, Lilly admits motherhood "fills your time but not your mind" ... so, while doing monotonous tasks like rocking the baby or pushing his stroller, she's had time to reflect on her failed marriage.

As you know ... Grande and Slater each left their spouses after meeting on the set of "Wicked" -- and they both finalized their divorces earlier this year, months after moving in together in NYC.

In the aftermath of the split news, LJ told us "I'm focused on my son and doing my best to navigate a spotlight I have never wanted or experienced before" -- adding she needed privacy to properly navigate through the issue.