hen the cycles after that go genetic/electric [where the dominant
species improves itself through CRISPR type technology] -> [currently
unknown event]
You would have eugenics war.
There would be safe monitored facilities where people could get standard well researched genetic modifications. However, they would produce results much slower as the long term effect of the modifications would have to be studied. Then there would be a medium risk group, and a high risk group of genetic alterations. They would provide more extreme modifications, but a higher number of them would go wrong. Some would end up say super strong, but now there are like 2 year olds mentally. The legit places would destroy them, but the less reputable might just turn them lose into a neighboring forest,desert, or etc. They could reproduce some faster than others. Eventually the modification would be understood, and most of them would be deemed bad. All but a handful would eventually be discarded, that were safe and needed. Most of the experimental places would go out of business because of bad reputations. Hay what happened to Joe? Last seen going into Genetic-R-Us.
Eventually herds of genetic abominations would roam the land. Now society, tired of genetic failures, would have raise an army to wipe out the failures. It would cost many lives as some of the failures are smart, or got smarter through inter species breading. Finally after many years of fighting society would stabilize again. We would again have spare resources, and the science communities would move away from genetics back to regular sciences.
At this point NASA re-emerges.
Space and NASA style solar exploration (nothing outside the solar
system) [at the end of this cycle, all life on other planets die out
except on the main planets moon] -> [see below]
Resource and land wars would slowly develop as more and more people move into space. The colonized planets will have habitable zones which will range from little to no protection needed to very expensive high maintenance protection needed. Rent would of course be high in the desirable zones, and low in the frontier lands. Class wars between these groups could easily develop due to unaddressed misunderstandings and envy or jealousness. Eventually the highly valuable resources would start to get depleted. At least the ones people could trade in for money. As soon as there were enough people who couldn't pay their rent or maintenance there would be wars over the habitable zone of the planet/moon. Many would probably die. The rich people would, having gotten even more rich and seeing the impending wars coming, moved off the planet moon to a new location. Possibly in their own ships, and maybe colonize their own moon,planet,whatever. The poor and middle class would primarily be stuck, but would take over the rich peoples houses as they have left, and whoever owns them still wants rent. The colonies would linger on in a state of subsistence, and people who died wouldn't be replaced to reduce shortages. Eventually there won't be enough people to do maintenance, and the places will crumble and most will die from exposure.
This is your most tricky requirement:
most medieval/tribal but with 'tech relics', early 1900s knowledge and
mechanical transportation. [At this point the dominant species has
split into three different breeds, through isolation and genetic
engineering to suit conditions]-> [currently unknown event]
The 3 species is relatively simple, you have the rich,middle class, and poor. Each will develop into its own species with corresponding more mutation due to cheap genetic alteration. They will breed, and through years of breeding form their own sub species. Obviously the rich, who can afford top notch genetics will be the most human, and advanced.
I can't think of a good reason why tech knowledge globally would drop that far.
The rich will hoard the best technologies, and the poor won't have access to many of them, but the tech and knowledge will be preserved. One possibility, you might not have enough smart scientist who can understand the science. Eventually the poor's genetics will become too degraded and start turning them into animals. The rich and middle class seeing this coming will wipe them out. Which is your wars for this era of people.
an unstable mess of sci-fi tech, people, ongoing squabbles over
borders and resources and a looming threat from the moon
Clearly this would be an automatic outcome from my story.
The rich survivors of the colonies would clearly fly back to earth, and have enough money to buy land, and re-settle. The people on the moon would clearly want to move back to earth once resource shortages start occurring. Either that or if they find themselves wedged between sides of a resource war among the other colonies as they start to die off. Being earth we would get first dibs on everything, and other would look on jealously at us. The moon would probably be the only ones would pose a serious threat. Many other ships coming back to Earth might simple run out of fuel, or the maintenance needs of the ships might overwhelm them. They would be in a weakened state and probably easy for Earth to take out should they become a threat.
Earth would still be the best preserved place in the solar system. Sure there could be some resource wars, but we will get our stuff from the outer planets,moons, or whatever. If push comes to shove Earth would have the most advanced fleet of well maintained ships, and would take what they need.