On the history of Planar Common
(note that in the following essay, I'm making a lot of things up - I'm not attempting to stick to what is known in canon)
The issue here is Planar Common, the dominant language in the City of Doors and other human-dominated planewalker communities on the planes. Where did it come from?
The Planewalker's Handbook (page 101) said that Planar Common descends from the Prime Common tongue, brought to the planes by prime explorers. In fact, it says "the earliest planar settlers from the Prime," which suggests that this couldn't possibly be the modern Common Tongue of Toril or Oerth or Krynn. In fact, it probably couldn't even be a human language. However, the Planewalker's Handbook also says "it remains understandable even by the greenest primes," which suggests that it actually *is* the same Common spoken on prime worlds - at least, on one of them.
The question, then, is which Common tongue is the ancestor of Planar Common? There are, as it happens, several.
Torilian Common is descended from Thorass, which is a pidgin of Jhaamdathan, Jotun (the language of Torilian giants), and perhaps other influences. While there have been many Common-speaking planar explorers from Toril over the centuries thanks to that world's plentiful supply of planar portals, I'm unaware of any Common-speaking planar colonies dominant enough to force planewalkers in Sigil and elsewhere to know the language. If Sigilians ever sought to learn Torilian Common, it was solely to communicate with people from Toril. And Sigil, as we know, long precedes the advent of Torilian Common, or even the Empire of Jhaamdath whose language inspired it. Sigil is at least 10,000 years old, while Jhaamdath was founded around 7,000 years ago.
Common on Oerth, a relatively young language, is a mixture of Suloise and Oeridian tongues combined with Ancient Baklunish to become an ideal language of trade. It is no older than the Great Kingdom of Aerdy, which was founded a little more than seven hundred years ago.
Still, Sigil and the planes have doubtless known many different "Planar Common" languages across the millennia.
Until 10,000 years ago, the nation of Azlant is thought to have been the very first civilized human nation, "uplifted" by aboleths so that those alien beings would have servitors among the dry realms. The Azlanti reached incredible magical heights and colonized a number of planes. It is said that pale reflections of their domain exist on hundreds of worlds, and examples of their architecture have been discovered on planes as diverse as the Plane of Water and the Abyss. Azlanti were a common sight in the City of Doors 10,000 years ago (especially as refugees from the Earthfall that destroyed their prime kingdom flooded the streets), and the archmage Shekelor was said to be among their number.
One of the greatest and longest-lasting of prime-based planar empires was Imaskar, which began its planar explorations beginning in around -8120 DR (9,490 years before the Faction War in Sigil) until the empire's fall in -2488 DR. In -4370 DR, a plague decimated much of the Imaskari Empire, suspected by some to have been sent by the Lady of Pain in retribution for Imaskari magic tampering with the City of Doors. At its height, Imaskar had colonies on countless worlds and planes, and it's not unreasonable to assume that their language made up the Planar Common of its day. Imaskar succeeded Azlant as the greatest mortal empire on the planes.
The next empire of note was Netheril, also from Toril, who explored the planes and ultimately colonized the Plane of Shadow via their city of Thultanthar circa -339 DR. Another Netherese city, Selunnara, is now in the Gates of the Moon in Ysgard. The Netherese began exploring the planes extensively during their Age of Discovery beginning in -1205 DR (2574 years before the Faction War). While Netherese planewalkers were a relatively common sight during this period, they did not construct any colonies of note until their gods moved the cities of Selunnara and Thultanthar into the planes just before the destruction of their land.
From around 3,000-2,000 years ago the Alphatians, natives of the doomed world of the same name, colonized a number of planes in the Great Wheel and elsewhere, and replaced Imaskar as the preeminent planar-aware empire in the Outer Planes. During roughly the same period, the dyoph armies of the Isles of Woe on Oerth conquered the City of Brass and thus began their centuries-long domination of inner planar travel. The Baklunish empire on Oerth warred with them for decades, their armies clashing only on other planes, but the doom of the Isles of Woe ultimately came from elsewhere. In the Deep Ethereal, the reclusive ethergaunts took exception to the probing of the Mage-Priests of Woe into their culture, and sent a terrible plague that only ended when the Isles of Woe was swallowed whole by the waters that surrounded it, and disappeared into the Ethereal and the ethergaunts' clutches. With their Isles of Woe nemesis out of the way, the Baklunish had less reason to travel the planes in numbers, and neither did their rivals the Suloise, and the colonies founded by both peoples slowly escaped their control. Still, the Suloise and Baklunish of Oerth remained a fairly strong planar force until the destruction of both their empires a millennium ago. For part of the following millennium, the Alphatian-descended Flaemish people were busy wandering the Outer Planes, traveling between planar communities and doubtless making their tongue commonly heard among planewalkers.
Having shifted from an Azlant-derived Planar Common to an Imaskari-derived one to a Netherese-derived one to a mingling of the tongues of the Isles of Woe, Alphatia, and the Suel and Baklunish, to a Flaemish patois heard in many planar burgs, to the war-torn tiefling empire of Bael Turath around 600 years ago, the last 500 years have clearly seen one Prime Material civilization influence the planes more than any other, and that's the world of Ortho, from which the Harmonium hailed. Particularly in the last two centuries, the Harmonium have dominated not only their own world, but perhaps a dozen colony worlds, the gate-town of Fortitude, and the entire plane of Arcadia to the extent that their philosophy has changed the basic structure of the plane. Of course, they've also risen to become one of the 15 great factions of the City of Doors, which decides what will be the Planar Common tongue more than anywhere else.
It seems clear, then, that Planar Common currently owes more to the common tongue of Ortho than anywhere else. As long-lived as many planars are, it's certain that words from older tongues will still survive, but for the most part Ortho sets the standard, to the extent that "even the greenest prime" from the world of Ortho can get by on Sigil's streets.
(Some of the liberties I took include working Azlant, from the Pathfinder world of Golarion, into the history of the Great Wheel, inventing a planar war between the Isles of Woe, Baklunish, and Suel, and incorporating Mystaran planar history smoothly into Planescape)
I'm interested in this topic generally, and as regards recent history I think it makes a great deal of sense that the current lingua franca of the planes is that of Ortho. The idea of a succession of "Planar Common"s based on ascendant planar empires is also quite adaptable to any history of the planes.
The existence of a cross-world "Planar Common" has always bothered me -- even on a single world a few hundred years and a few thousand miles suffice to substantially diverge tongues!
If you ever make any edits to this, I'd also want to know something about the influence of the very long-lived ancient races' tongues on the development of various mortal tongues; I would bet quite enough of them are bastardizations of Draconic that there's a whole family of mortal tongues that share Romance-like roots. With actual dragons still around to keep the tongue alive, it could well "rein in" some of the variants as they arise. Another possibility for a large cross-planar tongue source would be Auran, or Vaati, if we go by the presence of a Wind Duke empire in the 2e and 3e histories of the planes. Celestial is less of an option, as it is more likely dependent on human belief than vice versa!
As an interesting fantasy inversion of linguistic evolution, whatever ultimate tongue includes True Names and The Last Word (if this is even the same) may exert a unifying influence on language development; languages experience natural forces to diverge, but also feel a convergent influence on the spirits of the speakers from the One True Language. That could end up with the trade tongues of various worlds actually falling closer to one another, even to the point of mutual understandability.