There is no reason to assume that the Spellplague impacted other realities.
For several reasons
Crystal Spheres aren't part of The Realms campaign setting, they are added by Spelljammer.
First and foremost, understand that the concept of Crystal Spheres, and every other setting existing in a different one floating out in The Phlogiston is NOT core material to The Realms. It was added for the Spelljammer Campaign Setting as an optional way to tie all of the different settings together. In the FR wiki article linked in the question, note that the only source cited is the Concordance of Arcane Space...which is a Spelljammer Rulebook. The Planescape Campaign Setting offers an entirely different optional way to tie the settings together. This was explicitly done to let you play in multiple different settings with the same characters. It is, essentially, a hack applied on top of the Core settings.
The core settings (Forgotten Realms, Dragonlance, Greyhawk, Eberron, etc) all operate under the assumption that other settings either don't exist, or are sufficiently disconnected as to not matter. You never see a setting book explaining how this thing that happened in Eberron impacted these other things that happened in Faerun. They simply assume that the setting you are playing in is the only setting that matters.
Thus, outside of these two optional settings, travel between the two is impossible and Oerth and Faerun may not even exist relative to one another. (In a game played in Faerun, Oerth and 'Greyspace' may not exist at all). Based on that alone, each individual setting can be considered to be entirely cut off from one another, and cannot impact each other. Because without one of two optional campaign settings, no connection between them exists.
Nature of the Spellplague
The Spellplague was the result of a breakdown in the Weave of Magic caused by the murder of Mystra, goddess of magic. With no deity to manage the weave, it went rampant and caused a huge mess.
Thing is...
In Greyhawk, Boccob is the god of magic. In Krynn, it's Lunitari, Nuitari, and Solinari. In Eberron, there is no god of magic, magic is (theoretically) derived from Siberys, the golden ring around the planet (and dead progenitor dragon).
And, according to the Spelljammer rulebooks (concordance of Arcane Space p17-18) deities have no impact whatsoever on any crystal sphere they do not hold sway in. Unless they have a pool of worshipers there, or a powerful cleric who can make a connection, they can't interact with that sphere at all. The death of a god recognized in only one Sphere cannot impact another sphere.
Differing cosmologies
The settings in D&D are extremely different. In terms of settings that go into significant detail on cosmology...The 'World Tree' cosmology was something unique to the Faerun setting.
Greyhawk was left intentionally vague in terms of cosmology. Krynn Cosmology looks like this. Eberron Cosmology looks like this. Old Faerun Cosmology (World Tree) looked like this, and the new version like this. See how different they are? There's no way these are the same planes in the same Astral Sea.
In Conclusion
The simplest answer is that, according to the core settings, nothing that happens in one setting impacts anything that happens in another setting, because they are different settings. The fact that two additional settings (Spelljammer and Planescape) were invented to let you optionally glue them all together doesn't change the fact that they are entirely discrete settings with their own history and events that do not impact each other.
No
To open, lets look at a sample of the rules that say you cannot permanently kill such a creature outside of their home plane...
The only way to truly destroy a demon is to seek it in the Abyss and kill it there.
MM 51
Devils that die in the Nine Hells are destroyed forever
MM 67
Only on its native plane can a yugoloth be destroyed permanently
MM 311
Of note: Angels in the 5E MM do NOT have this protection. Weird as it may seem, it is actually easier to kill a Celestial than it is to kill a Fiend.
The nature of Astral Projection is that your Physical Body and your Astral Body are separated. Your Physical Body is left behind on your 'Home' Plane while your spirit goes walkabout.
Bringing Fiends and Celestials to the Prime doesn't work like that. When you summon one, it isn't just their spirit you are summoning while their true body is left behind on their home plane, you actually summon them.
The descriptive text for Demons on MM 50 says
Wherever they wander across the Abyss, demons search for portals to other planes.
The descriptive text for Devils on MM 66 says
Devils are confined to the Lower Planes, but they can travel beyond those planes by way of portals or powerful summoning magic.
In both of these cases, it is explicitly mentioning 'portals' as a way that Fiends find their way to the Prime. Portals are a way to physically move from place to place, not a way to send your spirit somewhere without your body tagging along.
Gate, in essence, is a portal that you create between where you are and anywhere else that can suck something through if you know their True Name.
Thus, a Demon who found a Portal to the Prime Material Plane and a Demon who was called to you through a Gate both, effectively, arrived on the Prime in the same way. They are both entirely and physically there. And because they are not on their Home Plane...they cannot be permanently killed.
Simply put...Astral Projection is the exception to interplanar travel rules - it is not the general rule. Plane Shift, which physically moves you to another plane, is only 7th level--compared to the 9th level Astral Projection. Astral Projection is special because it gives mortals the same degree of insurance when plane-hopping that Fiends and some Celestials enjoy naturally.
Just as a cautionary note, though: if you are Astrally Projecting, watch out for 'Silver Swords' (most commonly wielded by the Githyanki). Those can still kill you for real.
To sum up:
tl;dr:
The books say that a Fiend cannot be permanently killed on a plane other than their home plane. How they left their home plane doesn't matter.
Astral Projection is an incredibly powerful spell because it lets an Adventurer mimic that same feature via magic.
Best Answer
Only the following elements in the core rulebooks use the Astral Plane
While it's impossible to list every possible Astral Plane interaction in D&D, the list of things in the three core rulebooks which rely on the Astral Plane is actually very limited.
The following spells, items or abilities allow travel to the Astral Plane, and will not have that function if the plane is removed:
The only other core rules elements which rely on that plane are as follows:
You don't need an Astral Plane
Fundamentally, you can completely ignore the Astral Plane. The only significant changes you need to make are explaining how souls and planar visitors get to the realms of the gods, explaining where stuff gets banished by certain spell effects that normally send things to the Astral, resolving very high-level abilities that normally allow astral projection so that they work some other way, and explaining what happens when you place one Bags of Holding inside another.