I am no expert, but some thoughts:

It’s hard to answer without more detail on the definition of progressive.

For example, technologically and design-wise it’s a mix. We can use innovative, progressive techniques like natural cooling [example] (even if I would say it’s not technologically progressive, almost the opposite, I would say it’s definitely progressive design and incidentally a good thing). We can abandon technologies we considered progresses like hybrid cars and farming practices and embrace established tools like electric rail. Progress is a weird, relative word.

Overall solarpunk seems to be technologically progressive, even if aiming to regress the apparent massive progress made in our current systems; I argue that progressing into a dead end isn’t as progressive as partially regressing, changing direction, and progressing. It’s a very poor analogy, I realize solarpunk doesn’t aim to regress before progressing, but I think you understand my point that commercial rockets to put up TV channels isn’t my idea of progressive even if it was technologically innovative and unforeseen.

If you mean the mainstream label of social progressivism… it’s a harder questions, even disregarding the relativity of progress. Solarpunk will tend to attract people who have typical progressive social views, but I don’t feel it’s strictly inherent in any way towards the anti status quo, pro nature goals of the movement. Even the original punk movement had a minority of nazi subcultures who embraced the counter-cultural aspects. Are they punk? I would say not, but they can certainly feel at home unless they are made to be uncomfortable, which is obviously foreseeable due to the proven appeal of this movement and crossover with anarchism and other punk influence. (I realize ‘-punk’ is abused as a standard suffix in some subcultures misinterpreting cyberpunk, but I don’t think solarpunk is one of those. There is definitely some punk in it)

I think it’s inevitably going to be progressive as a design movement (unless recuperated to remove all meaning, which is a non-answer to your question), but in terms of social progressiveness, that’s only inherent in its main audience. I haven’t given this much thought and have little exposure to the theory and definitions, so do feel welcome to correct me.