I’d go as far as saying Advantage/Disadvantage is a narrative mechanic and Inspiration points are a way of triggering advantage
Not in general, though you have more of a point re: Inspiration. Advantage/Disadvantage at base is a simple way of expressing that there is some circumstance (which is usually part of the established game state/fiction) helping or hindering a given effort. An enemy being prone is part of the fiction, but it's not something the player arbitrarily establishes. Outside a Whimsy Card or something which gives him such control outside of his character's action.
If, say, I want my PC Able the Archer to have advantage when making a melee attack against an enemy, that can be achieved in a couple of ways. I could take in-character action to knock the enemy prone. I could ask my fellow party member, Bold Berthold, to knock the enemy prone before my turn, or to flank the enemy, if we're using the optional flanking rule. Or he could use the Help action to distract the enemy's attention, giving me a better opening.
If my group was playing with Lion Rampant's Whimsy Cards (1987) I might have a card that I could play to directly influence the narrative, including one which specified that my opponent tripped and fell.
I think the latter is an example of using a narrative mechanic, because it's dissociated from the actions my character takes within the fiction and directly alters a narrative element which is usually either determined by mechanics or the DM's purview to describe.
That's not true. Advantage or disadvantage is exactly like bonuses and penalties in previous editions. It is the result of specific tactical choices made by characters and the result of environmental effects. There is no mechanism in 5E for getting advantage for describing things. You get advantage on melee attacks against a prone opponent within reach. That's just a rule.
Yep.
The easiest definition I've come across is that a narrative mechanic is anything that works on or towards results that couldn't stem from something your character could do 'in character'. That casts a pretty wide net, but I'm also not using it pejoratively. That could probably stand to be reduced into a couple of sub-categories I think.
Yes, I think this one is pretty good.
I think Inspiration is kind of borderline. Treating Narrative as a quality of mechanics which exists on a spectrum, I guess it's a little further down the line than, say, making an attack roll. But I still think it's representing something within the fiction and internal to a character and their locus of control. The idea of BIFTs is to encourage roleplaying, right? Incentivize players to act out their character's internal motivations and defining qualities, and make them apparent to the table. Do so and the DM awards Inspiration. What does Inspiration represent in the fiction? To me, it represents a literal moment of inspired action. Motivated action. Extra focus and emphasis which improves the chance of success at a given action. We know both in fiction and real life people draw on internal reserves of focus and strength when inspired to do so. Inspiration represents such a moment, of increased focus, perhaps "flow state".