Sword of Spirit
Legend
Volo's Guide plays it too fast and lose the line between FR lore and 5e Generic Lore
Volo's Guide goes with generic D&D lore 90%+ of the time. When it specifically references a FR element, it directly calls it out.
In all of the 5e non-adventure books that have come out (except SCAG, of course), the default is generic D&D, and setting specific material is always called out.
Adventures specifically set in the Forgotten Realms probably just weave it in without making a distinction, but other books are fairly consistent in their approach.