In answering this I'm drawing heavily on Alex Golub and Jon Peterson, "How Mana Left the Pacific and Became a Video Game Mechanic".

There seem to be three waves of 'mana' entering Western popular culture and taking its current form. The first wave consists of science fiction from the Golden Age, whose writers used the word in several different senses, thus presumably making their readers familiar with it. For example Poul Anderson in Operation Chaos (1971) refers to the magical power of pagan religious symbols: "although centuries have passed since anyone served those gods, the mana has not wholly vanished from their emblems". Here 'mana' is indeed magical power, but it is not a finite or replenishable resource - you can't put a number to it. In the sense that Anderson is using the word, a cross repels a vampire because it has mana; it has a magical power inherent to it, which cannot be used up or transferred. Jack Vance (who of course is famous for inventing the entirely different magical system used in Dungeons and Dragons!) refers to 'mana' in "The Moon Moth" (1961) as a synonym for 'strakh', the personal quality which allows the Sirenese to wear particularly prestigious masks such as the "Moon Moth" or the "Imperial Dragon Conqueror". A man who goes about with an Imperial Dragon Conqueror mask without the strakh to back it up will find himself challenged to a dozen duels and, presumably, killed. The protagonist (and the reader) get an explanation of strakh early in the story, where the explainer simply lists a number of near-synonyms from Earth history:

Prestige, face, mana, repute, glory: the Sirenese word is strakh. Every man has his characteristic strakh, which determines, when he needs a houseboat, whether he will be urged to avail himself of a floating palace... or grudgingly permitted an abandoned shack on a raft. There is no medium of exchange on Sirene; the single and sole currency is strakh.

Here mana is not a magical quality at all, but some combination of personal charisma, forcefulness, and status; it inheres in individuals but cannot be used up or replenished (although you can presumably gain some by completing impressive works of art). Compare to 'whuffie' from Doctorow's "Down and out in the Magic Kingdom".

Then, in "The Magic Goes Away" (1976, won the Nebula the same year), Larry Niven introduced the idea of mana as a depletable resource. In this setting, magic only works where the land has mana, and each use of magic burns up some mana; thus in the distant past there were gods and dragons, but simply by existing they reduced the mana below the level at which their metabolisms would work. (Obviously, a dragon can neither fly nor breathe fire without using magic, the aerodynamics are ridiculous.) What's left supports wizards, mermaids, werewolves, and such less-intense but still magical creatures; then someone invents a spell to quickly use up all the mana in a small area... Parallels to the oil crisis are obvious. However, Niven's mana, while finite, is not replenishable, and inheres in land rather than people.

The next wave consists of roleplaying games and tabletop wargames - in the seventies the distinction is rather blurry. Now, Dungeons and Dragons famously uses "Vancian magic", not mana; that is to say, wizards memorise spells and then forget them on casting, and have to relearn them. (Sometimes this is instead presented as preparing the spell and leaving it hanging by going through all but the final few gestures and words required to cast it; in "Trumps of Doom" Zelazny has Merlin explicitly tell the reader that this is what he's doing. But the Merlin cycle is a mere Shadow of the Reality that is the Corwin cycle.) But in the "Chainmail" rules (1971) that were the precursor to D&D we find something much closer to a mana system: A wizard can cast between three and six spells per game, depending on their power, and these spells do not have to be chosen in advance as with Vancian magic. Although Chainmail does not use the term, you could regard this as a wizard having a set number of replenishable spell points, and each spell costing a point.

As mentioned, in D&D (first edition 1974) we have the memorisation system, where players choose before the scenario which spells they'll have access to. But the first edition was quite unclearly written, and it wasn't obvious that each memorised spell could only be used once; however, if you allow unlimited use, then even with the constraint of picking from a limited set in each adventure, the wizard will be fantastically overpowered. (Once-per-turn lightning bolts! Dragons wish they had that kind of firepower!) So the players set about house-ruling in limits, and several of them independently invented the replenishable-personal-energy system, variously called "goetic energy", "spell points", or "energy points". At this point we've got "mana" (though it's not yet called that) as a personal magic energy, which can be restored with rest and which is entirely separate from charisma or personal forcefulness, nor can it reside in objects.

The name 'mana', at the time sometimes spelled 'manna' in apparent confusion with the miraculous food from the Bible, is introduced sometime in 1976 (note that this is the year "The Magic Goes Away" is published and wins the Nebula - there was considerable overlap, then as now, between roleplayers and F/SF fandom), apparently independently by several people. The first seems to be the "Perrin Conventions", a set of house rules that gave "spell points" based on the STR, INT and CON statistics of the wizard, and noted that the system is "also known as the 'manna point system'". The same year, Gygax published the first psionics rules for D&D; in my experience psionics add very little to the game and break the true fantasy flavour, and in later editions they've been very off-again, on-again, but in any case they always use some sort of replenishable personal energy. Several now-obscure game systems and D&D variants using "mana" or "manna" as the limiter on magic were published in the second half of the seventies; for example, "Arduino Grimoire" by David Hargrave in 1977 and "Sword and Sorcery" by Greg Costikyan in 1978.

At this point 'mana', both the specific word and the concept of personal magic energy, is pretty well established as an RPG convention - even though the most well-known RPG, Dungeons and Dragons, used Vancian magic for its main caster classes. So now we can trace the third wave, which is computer games. As early as Ultima III (1983), the constraint on magic was "magic points", abbreviated "MP" - which to a later eye could just as easily scan as "mana points". (I'll note in passing that the Ultima series was immensely popular and influential, defining a whole genre of top-down adventuring-party search-for-the-McGuffin-while-killing-orcs games, now unfortunately in eclipse.) Then, in Dungeon Master (1987) we get the actual word 'mana'; this, again, defined the 3D-dungeon genre, which we find echoes of in modern FPS games in their "corridor-shooter" incarnations - you're going through the dungeon with a machine gun instead of sword and spell, but the geography is the same. Then in 1989 Bullfrog published "Populous", the first "god game", designed by Peter Molyneux - also known for "Dungeon Keeper" (another genre definer!) and "Fable"; if you follow computer games at all you probably know the name. At this point, I'd say the mana is fairly out of the magic pouch; in 1996 "Diablo" - still another definer of a genre - used mana and mana potions without, so far as I can recall, feeling any need to explain what it was.

How mana got from computer games into broader pop culture is not quite clear to me, and anyway would get us into the 20-year window; but I think I can gesture somewhat at the increasing mainstream-ness of computer games, perhaps especially World of Warcraft. If you like, gamers now have a lot more mana, in the sense of 'strakh', than they used to; and so others have picked up their usages and jargon. Alas, we have yet to acquire mana in the sense of energy usable for casting spells; but who knows what 2020 will bring?

To expand on the question a bit - It was used in the ‘magic points’ sense in Larry Niven’s ‘The magic goes away’ in 1976. But that’s hardly a pop culture touchstone. It’s not used that way in early role playing games such as Dungeons & Dragons or Tunnels & Trolls. Is there an early computer game that may have spread the usage?

Follow up question - how does the polynesian concept of mana compare to the abrahamic religion concept of manna? Both chronologically (as in, which one came first?) as well as the characteristics?

I hope the answer will also cover this: Melanesian, Polynesian, or both? If both, do we know which one originally?

Mana has always seemed to do 2 things, it explains what fuels magical power, as it is generally viewed as a finite magical power reserve inside of the magic user. So it explains where the magic comes from and how it can be used. Secondly, it serves as a balancing mechanic. Magic is supposed to be powerful and explosive and devastating and if the user could use as much as they want with no ritualistic cast time or use of some energy within themselves, then it would be too overpowered in any instance that it comes up. Almost universally whenever mana is in a game or a show or a story, it’s a limiting factor on the otherwise unlimited power of magic users, and so it fits perfectly wherever there is magic to use used, be it pop culture, video games, stories, etc.