There's an earlier question about the definition of steampunk, but the answers gloss over the 'punk' part of it, except for vaguely connecting it to cyberpunk. So is there any significance to the 'punk' part, or is it just a buzzword kind of thing?
The -punk in both cyberpunk and steampunk came from the punk in punk music, where punk originally referred to urban, raw, ugly, obnoxious, disillusioned, and disenchanted ~4 member rock bands who literally didn't know how to play their instruments and, subsequently, (post-punk) signified more or less that, but with more "cool" and a bit less "butt-ugly" to it as everyone learned to play and cultivated their image.
Your linked Q&A mentions that K. W. Jeter coined the term steampunk as a sly nod toward cyberpunk. To elaborate on that, people at the time saw Jeter's Dr. Adder as a cyberpunk novel--indeed, more punk (dystopian, urban, raw, and ugly) than most. And The Glass Hammer was even more clearly cyberpunk (i.e. it had a somewhat more explicit connection to computing). So for him to write Infernal Devices and coin the phrase steampunk to describe dystopian, urban, raw, ugly life in the steam age made complete sense.
The next two popular authors who claimed to be writing steampunk were Bruce Sterling and William Gibson. Their dystopian Victorian novel, The Difference Engine, although not as raw or ugly in outlook as Jeter's work, made computing an explicit theme and had a direct connection to cyberpunk in that Sterling and Gibson were both foundational figures in the sub-genre. So the label steampunk there made perfect sense as a pun. And what Sterling and Gibson had really done in cyberpunk was romanticize hacking. Their worlds were dystopic enough that you wouldn't want to live there, but the computer hackers who did were usually very "cool." So whether cyber- or steam-, they were writing technology in a way where you appreciated the machinic, knobbly, wiry, greasy bits for being sort of punk--at least, urban and ugly but still pretty cool.
The publication of The Difference Engine was a big event at the time, because Sterling and Gibson were huge, and that's really the book that--even though it wasn't so great--got the world to think of steampunk as a potential sub-genre itself.
Incidentally, Gibson once mentioned listening to Joy Division over and over while writing Neuromancer, so even though the term cyberpunk originated elsewhere, the -punk wasn't completely inaccurate or imaginary in relation to his work.
So while punk music had a very, very small but direct connection to cyberpunk and an obvious overlap in tone with cyberpunk, the connection to steampunk is a lot thinner, and all the -punk means (if anything) is that the steam age technology in it will be romanticized and cool ... and maybe just a bit gritty.
I believe the word punk is being used in "steampunk" and "cyberpunk" to refer to a dark gritty version of the prefixed "steam" and "cyber" terms. When cyberpunk started it was different from a lot of the science fiction to date because of how dirty and gritty the worlds and people inhabiting them were. That along with a "no future" or bleak future oultook tends to be a big driver in early cyberpunk.
In steampunk what I have seen are people embracing the punk portion with wild ideas that do not follow the norm. In this case "punk" is being used to mean "different" or to identify themselves as outsiders.
While Steampunk as a science fiction/fantasy genre is an outgrowth of cyberpunk, as a social, cultural phenomena it has a strong connection to punk music in its DIY ethos. Steampunk frequently features handcrafted one of a kind creations and/or modifications similarly Punk music culture placed a premium on self-production of music, fashion and fanzines.
"The “punk” part of the term has to do with the rebellious spirit and a Do-It-Yourself attitude that goes hand in hand with innovation. Early science-fiction writers like H.G. Wells and Jules Verne would have classified themselves as ‘futurists’ because their stories pushed the boundaries of technological innovation and explored new way humans can interact with their environment. The term Steampunk, of course, did not exist until long after stories like The Time Machine and 20,000 Leagues Under the Sea were already classics, but these authors provided the seeds that would some day branch into a popular genre that includes not only books, graphic novels and movies, but fashion, artwork, and handicrafts.