I think it depends on the ability. Is it a magic item that does it and the PC knows it recharges at dawn? Then it's not a narrative mechanic, per se. But if it's a metacurrency-type ability that the PC doesn't really know about and it's up to the player to deploy, then I'd argue it's a narrative mechanic because the player is using it to pick the point in the narrative where the PC has an unbeatable skill check.
What about something like the Lucky feat from 5e? It represents something, and it's something of which the character may be aware... and may actually be a universal force in the setting...
That makes every vancian spell, use of ki and second wind a "narrative" ability and I don't think that is what the word means.
I mean, there's an argument that is exactly what narrative ability should mean.
The lampshade of magic is what makes things non-narrative, because it becomes a quality of the character in the game world.
PF1 had something similar with the Well-Prepared feat. An awesome feat for low-level adventurers.
www.d20pfsrd.com
So this is an example that strikes me as odd because it is a quality of the character... it has a lampshade akin to the one we apply to spells.
Yet many folks would classify this as a narrative mechanic, but would not do so for spells.
Let's look at the kinds of mechanics that add something to fiction that wasn't there before.
Look at the game
Spire: The City Must Fall for a bunch of good examples of these kinds of things. Here are just a few class abilities that are in the game:
CUT A DEAL. You know anyone who’s anyone...
Once per session, set up a meet with an NPC who can acquire you pretty much anything available in Spire. It won’t be free, though, and odds are they’ll want a favour or a cut too.
SURPRISE INFILTRATION. Nothing can keep you out.
Once per session, insert yourself into a situation where you are not currently present, so long as there’s some conceivable way you could get in there.
LAY OF THE LAND. You are a trained hunter, and others would do well to heed your words.
When you enter a dangerous situation, you can name up to three features or opportunities that your allies can take advantage of. The first time you or an ally uses an opportunity, they roll with mastery (for example: cover with a good view of the battlefield, an exit, a badly-guarded door, a stack of barrels, etc).
DRAW A CROWD. You can pull together a crowd at a moment’s notice.
Once per session, you can draw a crowd to you in a matter of minutes. People will stop what they’re doing, so long as it isn’t life-or-death, and listen to what you have to say.
PUBCRAWLER. You bear an encyclopedic knowledge of where to get drunk.
Once per game, name a nearby bar, pub or inn where you know the landlord (whether they like you or not is up to the GM).
Each of the above are starting abilities for a class. Some have others, and they can all gain additional ones as they advance. The game gives a lot of power to the players, but all of it is based on the characters... none of it is purely a non-diegetic ability.