So to answer gyor's original question, does the Hand of Vecna in Avernus make Vecna a god in the Forgotten Realms...
The short answer is no, at least no more than he already was.
When you look at how the gods are orgnized in the 5e D&D multiverse, gods can be worshiped across many different worlds in the material plane, though they usually "reside" in one of the Outer Planes, or at least a demiplane.
Forgotten Realms, despite mostly being 5e's "default setting," does not have many gods who have influence beyond that world. The big exceptions are gods like Tiamat or Asmodeus, the former of whom actually originated from Greyhawk. I'm not sure of Asmodeus' origins but he obviously has huge influence on many worlds.
For Forgotten Realms, the reverse is also true, that gods that originate from other worlds (like Vecna, who is from Greyhawk) have little influence on that world. By "influence," I mean worshipers. After all, if you don't have any worshipers on a world, you have no one to carry out your plans.
The Hand of Vecna being in Avernus has almost zero impact on the Forgotten Realms, as the holder of that object (Arkhan) is to my knowledge not from FR, and has the Hand on Avernus which is not part of FR (no Outer Plane is, there are all separate and distinct from any world on the Material Plane).
Now if PCs took the Hand, brought it back to the Forgotten Realms, and started a Cult of Vecna there using the hand, Vecna could become a Forgotten Realms game, at least for your table. But none of this happens in the book.
As for Exandria (the world of Critical Role) it being mentioned does make it official in a sense. As for its gods, it's kind of pointed out how many gods from other worlds do manifest there, albeit under different names and different styles of worship (differences in world being common from world to world). Vecna of course has cults there, as does the Chained Oblivion (Tharizdun), the Scaled Tyrant (Tiamat), the Spider Queen (Lolth), the Strife Emperor (Bane), the Dawnfather (Pelor), the Everlight (Sarenrae), the Lawbearer (Erathis), the Lord of the Hells (Asmodeus), the Cloaked Serpent (Zehir), the Allhammer (Moradin), the Knowing Mistress (Ioun), the Matron of Ravens (the Raven Queen), the Platinum Dragon (Bahamut), the Stormlord (Kord), and others.
Long story short, no Vecna is not really a Forgotten Realms god, but you always have the option to make him one. He'd appreciate it I'm sure.
