Honestly, I think the skeleton of Asimov's story is very evident in the trailers. It's just that they have hung considerable meat on those bones that may not look like what old-time Asimov readers are expecting. They have definitely made some changes, like the clone emperors, but some of what you're seeing that doesn't look familiar may be because I think they are incorporating elements of the prequels, or at least of the second prequel, Forward the Foundation, into the story. For example, the young black man whom Hari embraces is, I am pretty sure, supposed to be Raych, his adopted son from the prequels. Also, IIRC in the second prequel there is considerable unrest on Trantor leading up the the departure of the group going to settle Terminus. I think they are also following the school of trailer production that says, put a lot of big flashy things on screen to draw in the Great Unwashed, and count on the Faithful to show up anyway.
I also saw a video where David Goyer talks more about the production over scenes from the new trailer. He does admit that they have not stuck absolutely strictly to the books but one of their goals was to make the story more intimate and emotional, which let's face it, the earlier books were not. He also said they very much wanted to steer away from the look and feel of the main pillars of sci fi movies that most people are familiar with, which are primarily Star Wars and Star Trek, with maybe a smidgen of Alien worked in. He said they challenged their visual artists to come up with a fresh look. That's an area where, at least basted on the trailers, I think they have succeeded in spades, however good or bad the show ends up being. Some of these planetary scenes in the trailers look like science fiction made incarnate, or at least my perception of it. Example, the ringed planet, which is the homeworld of Gaal Dornick. Stunning. He also said they shot on real locations, and for effects with miniatures instead of CGI, as much as possible, to make it feel real. As an adaptation, it may end up bleh, but it's going to look epic, IMHO.
All that said, we were never going to get a 100% faithful, literal adaptation of the Foundation books. I think if we have the mindset that this is a fantasia on Foundation, in the musical sense of improvising on a melody, and stay open to it, we will be entertained. He didn't say this in so many words, but I caught a strong echo of Peter Jackson from 20 years ago, saying that job #1 was to tell a good story and job #2 was fidelity. Most of us were reasonably pleased by the results of that approach to LOTR, and I am certainly willing to give Foundation a chance. If nothing else, remember that at one point not that may years ago, ROLAND EMMERICH was going to be making Foundation, and ponder how good a movie that would have been. I imagine it would have been along the lines of the dismal Starship Troopers movie, at best.
"Olorin I was in the West that is forgotten...."