It's effects may as well be magic.
Most D&D spells either create something out of nothing, or call out powers beyond our own, and yet most D&D spells also are easy to resist.
None of those things are true for Grisha powers.
If a Heartrender is stopping your heart, you can't "make a saving throw", the only way to stop them is to interrupt them (usually by hurting them or grabbing them) or break LOS (and not for like a second or two but round around a corner - in the show even that doesn't work - and in the books very powerful Heartrenders don't even need LOS)
In D&D you can run out of spells. That's not true for a Grisha. They can keep going until they're exhausted, and that's a very long time for most Grisha. They just keep doing their thing - and they're more powerful than D&D allows for - a Heartrender is just not something D&D can handle, because they don't do HP damage, they just instantly kill people, and even ones who aren't good at it don't just minor damage - they're still lethal - either they stopped your heart or broke your neck or they didn't - and if they didn't, it's probably because you interrupted them. And six seconds? They stop a heart in a lot less time than that, so it's not like they have a multi-turn wind-up.
Inferni can just keep blasting fire. Squallers can keep up powerful winds for hours on end. Tidemakers can, well, make tides - they can affect vast volumes of water for extremely long periods of time.
And they can innovate with their powers too, and come up with new stunts and new ideas. That just doesn't work with a system with need little discrete packaged spells.
They're "balanced" because they're facing people with rapid-firing guns (though most Ravkan Grisha are wearing bulletproof body-armour - the kefta is essentially bulletproof to a significant degree - this is downplayed in the show, but sometimes it works - and they can still be it in the head, legs, hands, or just hurt by the force of impacts through the armour) who can also kill people instantly.
The closest thing any game has come to them would be the
alternative rules for Psions in Aeon/Trinity (I think they're in the player book).
And again, whilst we haven't seen in much in the show, D&D-style magic does exist in that universe, it's just Very Bad (c.f. Nichevoya etc.).
I know that Grisha do not cast spells in the D&D Vancian sense of the word, but I'm trying to use the system we already have, with some twinks, to allow play in the world of the books and show.
Okay but D&D 5E doesn't have the tools for that, because it doesn't have a psionics system, and the spells we have right now don't fit at all well with what Grisha can do.
Again, D&D-style magic does exist in the books, and it exists in opposition to what Grisha can do.
If you wanted to do it in 5E, you'd need to build a new class. The best thing to do would be to build it from the ground up, perhaps using a 3PP Psionics system as a starting point. If you insisted on using existing spells, you'd get something that's never going to seem much like a Grisha, again because even an inexperienced Heartrender is at once vastly more dangerous and vastly more limited character than 5E allows for.
And skill is a huge part of being a Grisha - Corporalki are perfect example - all Corporalki and do all three different Corporalki things, but they aren't equally good at them - and it's matter of skill - not like, limited spells per day - they're worse at them. 5E has no mechanic for that.