The Black Pits are not games. Dark Alliance are not games of the main Baldur's Gate series.
Despite your beautifull english sentences you obviously don't know much about BG1/2 but you're arguing about "the definition of a Baldur's Gate game"... Interresting.
I asked if they are Baldur's Gate games. The title on them is Baldur's Gate: Dark Alliance1 and 2. Its been accepted that they are part of the Baldur's gate series as they take place in the city or around it.
But according to your definition they are not. Even though they are considered good games on their own. That's Gatekeeping btw - which is pretty awful behavior. WoTC has established a fairly straightforward definition of what a BG game is, with a fair degree of latitude to establish storylines. That's called setting precedence.
Objectively they (WoTC) would be the authority on this sort of thing. They granted a License to Larian not only because of the licensing fees offered but because they presented a solid story that *they* felt honored the series appropriately and they had the game-making chops to create a worthy sequel. Initially Larian had been rejected - just to get ahead of the ungenerous assertions of "because money, duh" - because they felt Larian wasn't ready.