for us non-americans, can someone please explain what general political aims the 'moderate' and 'progressive' parties represent? And where are they on the republican democrat spectrum?
The "progressives" generally want to limit gentrification, prevent renters from being evicted, and add more subsidized housing. The "moderates" generally want to make it easier to build more housing of any type. You could broadly characterize the two groups as "default skeptical" vs. "default supportive" of real estate developers.
But housing is only one point of disagreement (albeit one of the most significant), plenty of people have more nuanced positions than this, and these camps are not entirely uniform across issues. Other points of recent disagreement include Covid lockdowns, what the school board should focus on, how hard prosecutors should go after police misconduct vs. minor crime, responses to the homeless, how much power the board of supervisors should have vs. the mayor's office, ...
It's not fair to say that the progressive group primarily consists of "NIMBYs and nostalgic boomers", nor is the group cohesive enough to label anyone's individual comments as representative of a "they"; if you are going to characterize either of these groups negatively you should try to quote specific comments and attribute them to specific people, rather than making vague insinuations.
I think you offered charity to the point of being misleading. There is only one side who wants to make housing more affordable. The charitable view of progressive policy making is that they reject any demand for San Francisco to be a commercial center and want to preserve the lifestyle, built environment, and composition of residents to what it was in the 80s.