One you didn't mention that I have read multiple examples of is 'Clockpunk', which is what you get if the stuff Leonardo DiVinci imagined in his note books was worked on until it became viable inventions.
Also, it should be noted that many of these genres are not necessarily set in an alternative past. For example, 'Clockpunk' includes any setting missing all forms of motive power that don't rely on animal effort, including various versions of post-apocalyptic dystopias where for whatever reason all fossil fuels are gone and people seem to have forgotten how to make electricity (or for some reason can't).
Some examples would 'Souls in the Great Machine' by Sean McMullen and Paolo Bacigalupi's 'The Windup Girl'.
Personally, I find 'Clockpunk' unconvincing as a science fiction as almost any sort of harnessing of energy is going to be more powerful than mere human effort, and complex machines depending on human effort are unlikely to be more useful than simply unencumbered bodies. Almost every example I've seen offends me as an engineer however well written it may be otherwise.
I've also never encountered the concept of 'Formicapunk' until you mentioned it. I did some digging, and mostly I can find the concept lambasted by people as a complete failure to understand the genera's principles conventions.
'Punk' arose out of extrapolations of what would happen if technology was largely unchanged except a particular area advanced independently to some logical extreme. Initially this Cyberpunk 'forecasting' what the near future implications of a fully digital society might be - a society that generally seemed stuck in the 1970's or 1980's social crises but also had this advanced computer technology.
The other versions arose by looking back into the past and imagine what might happen if certain inventions which were not fully realized at the time had been made viable and socially important, causing a society to be based around those inventions while critically other inventions were not discovered. For example, 'Steampunk' involves assuming inventions like Babbage's Engine are fully realized and mechanical clockwork computers become a big thing, but society does not go on to immediately invent electricity or the internal combustion engine to replace steam engines or mechanical clockworks. The genera doesn't refer to just getting stuck in an 'era' like 'the Victorian Age' or 'the 1970's'. It's about extrapolating technology and imagining what the world might be like if that technology exists, usually in the context of the social upheaval associated with new and rapidly improving technology. Originally 'Future Shock' - an idea very current in the 1970's - was very much part of the concept.
