the Kai goes through the wormhole and becomes essentially immortal/dead,

Actually it's the ARTIFICIAL MICROBES that RESURRECTED KAI OPAKA again:

https://memory-alpha.fandom.com/wiki/Artificial_microbe

An artificial microbe was a microorganism which was created by any process except natural ones (that is, biologically).

In 2369, Captain Benjamin Sisko, Lieutenant Commander Jadzia Dax, Chief Miles O'Brien, and Doctor Julian Bashir encountered artificial microbes in the atmosphere of a moon in the Gamma Quadrant were an Ennis/Nol-Ennis penal colony was located. The artificial microbes regenerated those who had died on the moon, becoming a curse to the two warring factions.

After Bashir had studied the artificial microbes aboard the USS Yangtzee Kiang, he determined that once they had regenerated a lifeform from death, that lifeform could never live in any environment except on that moon without suffering immediate death. As a result, Kai Opaka, who had been so revived and did not wish to die again, elected to remain on the moon and work to bring peace to its other inhabitants. (DS9: "Battle Lines")

And since she probably also knew she wouldn't be coming back to DS9 again, the gift to the daughter of MILES was probably just a going away gift that she knew she wouldn't be needing anymore in her new life.

And The reason why one suspects she knew what would happen to her is because she also knew her PAUGH and SISKO's would encounter each other again.

https://memory-alpha.fandom.com/wiki/Battle_Lines_(episode)

Sisko begins to tell the Kai that if they ever find a way to get her off the planet without killing her then they'll return, but Opaka interrupts him and tells him that her work is now on the moon. However, her and Sisko's pagh will cross again.

https://memory-alpha.fandom.com/wiki/Pagh

The Bajorans believed that the pagh was the spiritual force inherent to all sentient beings. Their belief was that the Prophets replenished the pagh from their Celestial Temple. Bajoran spiritualists were apparently able to assess the strength of an individual's pagh by grasping their ear. (DS9: "Emissary", "Accession") The pagh leaves the body after death, leaving only an "empty shell". (DS9: "Indiscretion", "Ties of Blood and Water")

So we have a DS9 TREK STORY that NEX says he enjoyed watching ...

that's partly about the RESURRECTION of a character by these ARTIFICIAL MICROBES ...

yet whenever PICARD is RESURRECTED in that TREK STORY ...

NEX has a MAJOR HISSY FIT ABOUT IT ...

and claims that it MAKES NO SENSE.

But when has THE RESURRECTION of ANYTHING ever MADE any SENSE???

It MAKES NO SENSE, but RESURRECTION has also been an EFFECTIVE STORY TELLING DEVICE for quite some time (as was also illustrated in the REMAKE of BSG).

Plus ANCIENT EGYPTIAN MYTH has RESURRECTED characters as well.

Osiris - Wikipedia

https://en.wikipedia.org/wiki/Osiris

Osiris is the god of fertility, agriculture, the afterlife, the dead, resurrection, life, and vegetation in ancient Egyptian religion. He was classically depicted as a green-skinned deity with a pharaoh's beard, partially mummy-wrapped at the legs, wearing a distinctive atef crown, and holding a symbolic crook and flail.

And it also remains a MYSTERY why it's suppose to be OK for BSG and for DS9 and other ANCIENT MYTHS to tell us RESURRECTIONS stories, but it's NOT OK for PICARD.

@Knixon said:

In the early first-season episode "Battle Lines," before the Kai goes through the wormhole and becomes essentially immortal/dead, she gives her necklace thing to O'Brien for his daughter.

Do you suppose that was meant as some kind of foreshadowing that they wound up deciding not to pursue?

I wonder what they might have been planning?

No the script said so

Yes, well, the scripts have foreshadowed in the past and then changed. Such as the alien parasites things near the end of TNG season 1, that got retconned (rather badly, I think) into being the Borg.

Well the aliens from Conspiracy would be an interesting foe for a Trek show that takes place in the future.