The move from group stage to league phase is a big move actually since big teams have a chance to be pitted against each other even from day 1 of the competition. I know we had some match-ups like this in the past format but it should be more frequent with league phase. For the league phase, I understand that teams position in their last domestic league table is used, not sure about the qualification rounds currently going on and there are mention of 4 slots with criteria I'm not too sure of on the uefa article you posted.
Yeah, maybe you are right about that. Not exactly a league but a different variation of it now. We are all going to experience it for the first time so I hope we enjoy this format more.
When it comes to the qualification rounds going on currently, you know in so many leagues there are qualification slots given to teams. They need to get past a couple of rounds successfully to have a chance to play in the league phase.
Biggest European leagues don't generally have this, they are sending their teams directly. I guess this is why you were surprised to see it.
Lastly when it comes to 4 extra slots, some big European leagues were given extra slots depending on club coefficients etc.. For example a league normally sends 4 teams but the 5th finishing team also gained a chance.
Bologna and Dortmund qualified thanks to that but I'm not sure about the remaining 2 slots. 
I know it's complicated but you would get the logic better in time.https://www.uefa.com/uefachampionsleague/news/028a-1a386150ed4b-322dff667686-1000--2024-25-uefa-champions-league-bologna-and-dortmund-secure-/