The Twist Is Oils, Not Juice
A lemon gives a drink two completely different things from two different places. The juice is acid and sugar. The peel is aromatic oil, and that is the part you smell before you ever taste the drink.
Watch a good bartender finish a Martini or an Old Fashioned. After the stir, they cut a strip of peel, hold it skin-side down over the glass, and give it a sharp pinch. A fine mist sprays across the surface. They might wipe the rim and drop the peel in, or they might discard it entirely. No juice goes anywhere near the drink. That gesture is doing real work, and it has nothing to do with sourness.
Two ingredients from one fruit
A citrus fruit gives you two separate things, and it helps to stop thinking of them as the same ingredient.
The juice is the watery interior: acid (mostly citric), a little sugar, and the sharp wet sourness that balances a sour cocktail. When a recipe wants to cut sweetness or add tartness, it wants juice.
The peel gives you almost no acid and no sugar. What it carries is aromatic essential oil, and the dominant one in most citrus is limonene, alongside a supporting cast of other volatile aromatic compounds. These oils are intensely fragrant and barely soluble in water. They are the smell of a fresh orange when you break the skin with your thumbnail, before any juice is involved.
Those two parts live in different places and do different jobs. Squeezing in juice and expressing a peel are not interchangeable. One adjusts the taste. The other adjusts the aroma.
Where the oil actually lives
Cut into a piece of citrus peel and you see two layers. The colored outer skin is the flavedo, and that is where the oil glands sit, little reservoirs packed just under the surface. The white spongy layer beneath it is the albedo, the pith, and it holds almost no aromatic oil. What the albedo holds is bitterness.
This is the whole reason a zester or a careful peeler beats a knife that digs deep. You want the flavedo and as little albedo as possible. Take too much pith and you trade fragrant oil for a flat, bitter note nobody asked for.
When you express a twist skin-side down over the glass, you are rupturing those oil glands in the flavedo and spraying their contents across the surface of the drink and up into the air right under the drinker's nose. Aroma is most of flavor, so that mist changes the drink before the first sip touches the tongue. That is why a citrus twist registers as smell first.
The flamed peel, honestly
You may have seen the bit of theater where a peel is held over a lit match and pinched, sending a brief flare through the spray of oils. It looks great. The honest accounting is that the effect on the drink is modest. Limonene and its companions are flammable, so a little of the expressed oil ignites, and the brief heat does change some of those volatile compounds and add a faint toasted note. But most of what you are getting is the show. A plain expressed twist delivers the great majority of the aroma. Flame it because you enjoy it, not because the glass demands it.
One practical consequence of all this: the oils are volatile and fragile. Bottled juice keeps some usable acid, though it dulls, but dried peel and old zest have lost the very thing that made fresh peel worth using, because the aromatic oils evaporate. There is no shortcut here. The twist works because the oil is fresh and you just broke it open over the glass. Cut it last, cut it shallow, and express it where the drinker can smell it.