Yep, the tone of the Forgotten Realms as a setting *really* depends on the GM/writer/game dev. All the FR based games I've played have had different tones. Icewind Dale 1 and 2 feel isolated, desolate even. Baldur's Gate 1 is goofy but also mysterious. Baldur's Gate 2 takes the undercurrent of darkness present in BG1 and dials it up. There's still some great humor, but the tone is much more serious. NWN2 is a pretty classic feeling fantasy adventure; MotB again dials up the darkness and, as I recall, felt quite mature in its themes.

BG3 leaning more toward "silly" (but with some dark shock value type elements) is due to Larian's take on the setting, not the setting itself. The FR as a setting is incredibly comprehensive, and obviously juggles a lot of elements that can clash with each other and be like "Frankenstein's monster" in the wrong hands, because a story needs focus. A good GM narrows down that focus, sets a tone, and tells a story with the appropriate elements. (And while I'm not the biggest fan of BG3's story, I'm not implying Larian failed here, because obviously they got a lot of people into the setting who weren't before).