Have you ever thought about how teleportation works? Because it's imaginary, we don't often wonder about the details. It's magic, and that's good enough. Usually. Unless, that is, you're playing a game relying on a series of logical connections to render a predictable and repeatable result. In real life, that's called science and it works marvelously well (you're using the result of years of science to read this very article, in fact.) In a fantasy world, we get to make up the rules, but we still strive usually for consistency, and so people think about the implications of an imaginary universe a lot.
In fact, it's been argued that maybe some of us think about it a little too much. Maybe because of that, the 5th edition of D&D has promoted a somewhat simplified view of its fantasy world compared to previous editions. There are fewer details about how and why things work in 5e partly, I think , because there's relatively little official content for 5e. In previous editions, there were "splatbooks" about practically everything. There were books like Guidebook to Clerics and Paladins, The Complete Warrior, Planewalker's Handbook, Guide to the Astral Plane, and so on. If there was a topic you were interested in as either a player or DM, you could find a book about it.
There's a lot less of that now, which I don't mind because I don't love the thought of repurchasing essentially the same material with some slight adjustments to the math and timeline. But sometimes, a question arises that actually matters to a game, and it isn't clear whether there's official governance or guidance.
In previous editions of D&D, it was explicit that the teleportation spell transferred you from one location to another by way of the astral plane. In other words, the process was this:
This was explicitly stated (not in so many words) in at least D&D 2e, 3e, and Pathfinder.
If you look for this in 5e, though, you'll find (almost) no confirmation of it. For all we know, teleport could be a space warp effect in 5e. Maybe you cast the teleport spell, causing the fabric of reality to warp such that two disparate points move closer to one another, allowing you to step from Waterdeep to Baldur's Gate in the matter of milliseconds. Or maybe it's a time freeze effect, allowing you to pause time while you hurry from one location to another. It isn't explicitly explained in 5e.
Believe it or not, this isn't just me being pedantic. A game I was running involved some planar travel, but the astral plane specifically was not accessible. It occurred to everyone in the game that this meant teleport would be impossible, which had the potential of seriously affecting tactics.
I did some research online and found an rpg.stackexchange.com post posing the question. The answers seemed well thought out, but it jogged my memory and I realised that I think I actually had the right answer myself.
In the Dead in Thay adventure from Tales from the Yawning Portal, there's evidence that teleportation does involve interdimensional (planar) passage.
On page 110 (abbreviated for brevity):
Magic secures the dungeon [...] no spell permits teleportation out of the zone in which the spell was cast.
The use of the subheading "Dimensional Barrier" combined with "no spell permits teleportation" suggests that teleportation is blocked because passing through a different dimension is made impossible. There's no mention of the Astral Plane specifically, but that's still a strong argument that the teleport spell in 5e involves some other plane.
Yawning Portal is an adaptation of previously published modules, so you might suspect that the Dimensional Barrier subheading slipped in unnoticed. But Dead in Thay was written for D&D "Next," which is what 5e was called before it was called "5e." And besides, if we can't trust official material, what can we trust? For added support, though, I did look for Yawning Portal errata. It does exist, but Dimensional Barrier has not been redacted.
Based on previous editions, and a lack of any other logical plane, it makes sense that teleport in 5e would use, specifically, the astral plane to make instantaneous movement possible.
Barring Sage Advice, errata, or some other explanation of the spell in future publications, I'm pretty happy with this explanation.