CurePikachu said:
If we go through with this we will need to replace the existing implication Baldur's Gate has to Dungeons & Dragons before doing the BG -> forgotten realm one
Good point, that's probably too much.
I decided to step back and take a look at all of the Dungeons and Dragons content. Here are my findings.
Looking at the posts in Dungeons and Dragons I see (in order of popularity)
1) Baldur's Gate/Baldur's Gate 3, which is in Forgotten Realms
2) Original characters
3) Critical Role, which takes place in a world called Exandria, but uses the Forgotten Realms pantheon.
4) Planescape: Torment, which is in the Forgotten Realms
5) Shadow Over Mystara which takes place in the setting Mystara
6) post #397286 has Erandis d'Vol, a character from the Eberron setting.
(since I can't search for more than 2 tags, I have some trouble checking thoroughly, hopefully I didn't miss anything)
Edge cases:
Many deities and some characters, notably Vecna, were brought over from the Greyhawk setting to Forgotten Realms.
Similarly, Critical Role used the Forgotten Realms pantheon. Consider post #6216629 which shows Forgotten Realms deities fighting in the Critical Role continent of Exandria.
post #3669135 features original characters from a campaign played in the Ravenloft/Curse of Strahd setting, who are also visually flavored towards that setting. However, it features no canon material from the setting, so you wouldn't be able to say that it's curse of strahd without reading the caption.
Mystra and Shar are both Forgotten Realms deities, but their only posts on here are portraying their appearances in Baldur's Gate 3.
Summary
Forgotten Realms only characters: Zariel, Elminster Aumar, Volo, Iymrith.
Characters shared by multiple settings: Tiamat, Asmodeus, Gruumsh, Vecna, Bahamut, Lolth
These characters are from the Forgotten Realms, but also canon in Critical Role: Mystra, Shar, Eilistraee, Myrkul
Closing Thoughts
Campaign settings in D&D, broadly speaking, serve to define the aesthetic of the game. Forgotten Realms represents the most iconic and popular high fantasy Dungeons and Dragons that most people expect. Other settings, like the steampunk Eberron, gothic fantasy Ravenloft, or sci-fi Spelljammer, have little to no content on this website. This means it's not especially useful to have an all-encompassing Forgotten Realms tag, so I think we should drop it entirely, and use dungeons and dragons as a replacement as needed.