The story in BG3 takes place after Descent into avernus so the story doesn't connect both games,the setting does however but it's not enough,otherwise Dark Alliance and Demon Stone would have been BG3,4 and 5 for example.
Just because the other games weren't titled BG3, BG4, etc, doesn't mean they could not have been (if setting is enough). BG3's story can be made to connect to BG2. Whether they have done so or not we just cannot know yet.
I meant P.K is closer to BG than BG3 I wasn't rating P:K or comparing it to DOS2
Even a racing game can be called BG3 if WoTC really wants to but those games weren't named like that for a reason. They said the story of the first to games was totally closed,and that some people in FR are very long lived so we could see them in BG3. I don't think a couple cameos are a solid link to a story but yes,we don't know about that yet so everything story related are just guesses.