I would like to share my own experience after reading all of you.

Pathfinder kingmaker is, for now, the game the closest to the BG-feel and here is why for me.

First I would like to talk about the level-up aspect of the game.
I remember the first time I play, it was so hard at the beginning. But at the same time I was really charmed by all the possibility I have to develop my team.
Each level let you free to choose where you go and after few games I became familiar with the gameplay and so I could tried many funny things.
And each charm had his charm, his particularity. So this is one of the reason which make me play again and again.

What make me leave the game first was the realm management. I was SO happy to have a realm to manage ! This is why I couldn't get how, despite of all my efforts and vigilance, I ended up ruined, game over. So harsh. It's, maybe one of the biggest fail for me. All the game I played after I put the realm difficulty at the lowest and I found it still not dat easy...

The combat are the second point which give me this BG-feel. I played RTwP (cause obviously I like it) and it was just like BG. The fight begin, everybody move and shot and fight and I pause, think, give orders and let's go (before I pause one sec later xD).
This point, I insist is crucial for a game who would be a successor (or wathever the name you want to use. Someone said me BG3 was not a successor but a sequel. I don't really get the point but maybe it's the langage barrier). I really appreciate, from BG1 to pathfinder, the flow you can have with RTwP. It feels so more real (can't get the people who said turn-based is more real. :-/)
So I enjoyed the fights in pathfinder cause there was intense, hard, with lot of spells and move from all the party.

The story. Honestly, I think I'm in a way really demanding about this point however I'm ever surprised by how people easily trash-talked about the story of the games.
People should remember that it's hard and harder to create original synopsis and it's not really a problem. I mean, a lot of really great stories have a pretty basic synopsis. What matters is how the story is narrated.
So, I appreciate pathfinder, appreciate the treason, when we had to choose between two companion quests. I appreciate the narrative, the bitch who played with me, etc etc.
Sure, there is ever a moment when you think "I would have had the opportunity to do it" but we have to be humble and a little cooperative sometimes.
By the way, I ever loved the story of BG1, loved the one of PoE 2, really loved the one of the Witcher 3... Well.. Wait... I'm looking for a story I didn't appreciate.
I know ! Assassin's creed story are the worst ! I love the games but can't stand the narrative which is dramatic fro my point of view.
About BG3, I'll wait to see. As I already said, the story looks classic at first but we could be surprised so I'll be patient and won't judge on EA a "looks-like-pretty-classic-story". MAybe it'll be awesome, maybe it'll be "meh". Wait and see !

In pathfinder I really appreciate the companions ! there was interesting, some archetype and some others who was not. They had good side quests and even some amazing surprise (Ho Tristan why... :'( ). Even the romance was good, they came step by step and we could feel the companions know what they want.
And yeah it's a direct critics against BG3. The romance so far are really deceiving. I give a staff to Gale so two days later he wanna blow mine ? Seriously ? I let Astarion suck my neck so two days later he wanna... well you get it. This is not romance, this is strange nymphomania.
Well.. Maybe it's cause of the tadpole !!! What a twistplot.

In Pathfinder, I love the freedom we had to explore. It's ever a little confusing but this is a big part of the pleasure.
This is something BG3 doesn't give me but it's still EA, so maybe with more content we will be able to travel wherever we want ? I hope so. For now, it's a little to directive.

To conclude, for me, the BG-spirit is a good balance between :
- character with lot of classes and level-up possibilities
- freedom to explore
- flowless fights (not fast and furious, but at least not slow and tedious)
- strong main story, well-narrated
- memorable companions

Maybe I forgot something, but at the moment this is the 4 major elements I'm looking for.