Not exactly.
The Democrat plan was for the Iranians to give up their nukes and for Iran to try to re-engage with the rest of the world on a more normal footing.
There is a deeper layer to this plan.
The normal footing is that Iran is free to realize its regional imperial ambitions through any non CRBN means - including proxy warfare and terrorism - without meaningful interference from the other signatories of the deal.
It is not stated explicitly into the deal, but it is technically implicit out of purely practical, predictable actions and reactions.
Any attempt to severely sanction Iran for whatever reason and in any way while the deal is in power was going to get Iran to object that USA is not keeping its end of the deal (not sanctioning Iran), and hence it will cease to follow its own end of the deal too (working on building nukes), so centrifuges go BRRRR.
Its hard to say for sure if the Democrats are totally fine with that, or are too stupid to realize that this is how things are going to go with the deal, you can probably find people willing to believe either case.
The hope was to establish a new balance of power between Saudi Arabia, Turkey, and Iran.
Yes, that would be one of the effects. With Iran being much more powerful, and taking out a significant portion of the oil monarchies influence in turn. If not taking them out more literally.
What the Democrats want is not to be involved, but not let the whole shatterbelt go to hell. But without raising troop deployments, that's not likely to work out.
Why not both? Its perfectly possible for the deal to be kept, DNC run USA not get involved, and shatterbelt to go to hell, as in Iran carving out a little empire they feel they deserve, as the Democrats send half hearted appeals for peace and virtue signal in the UN.
Trump broke from this agreement, because Iran also has a very robust ballistic missile program. Trump felt that was too much of a threat to keep, so he demanded they nixed it. They told him no and it escalated from there.
That also has a deeper layer, that goes into military technology\strategy.
Namely, everyone knows that ballistic missiles are an extremely suboptimal type of artillery in terms of cost effectivness. They are glorified terror weapons, and very expensive ones.
On top of that, with the rise of ABM systems, they got even worse.
The only way ballistic missiles can be worth their price is if you have a plan, or at least want to make the designated targets scared that you do, to put some kind of CBRN warheads on top of these missiles, with the N being the top of the 4. Hence, if you assume that Iran is bluffing about going for nukes, then it either needs to continue the bluff, or the threat value of their expensive missile program is going to be meager, making it a huge waste of money for a country that doesn't exactly shit money these days.
But if they aren't bluffing and the promises of not working on nukes they give are lies and delays, then it makes perfect sense for Iran to continue maintaining and advancing a ballistic missile program.