Robots are one of the fun opponents of stranger sf apocalypses. Personally, I recommend 2000ad comics (Robusters/ABC Warriors especially) and John Sladek (the best SF robot philosophy guy). Many robots are simpletons living as if the apocalypse never happened as best they can. Many over some time have upgraded and improvised themselves and operated beyond their warranty period. Many have developed interesting personalities and mannerisms and many towns have a robot district where free-willed robots and their less optimised kindred dwell. Sometimes these have signs of poverty, beggars needing a recharge and even gangs of robots. Local robot towns may vary.
d12 Robot Tribes
These robots act out their desire to serve humanity and are unaware of the apocalypse thanks to space colony standards becoming the norm. Mostly they are pacifists but may be annoying especially ones spruiking products or offering addictive games. Many don't last long outside their ancient structures as they may get shot for parts or taken as both treasure and slaves to be reprogrammed. The more flexible robots with accept the present and serve a new human owner and display more independence. In a way these robots are the original tribe
2 Code Blue
Police and security robots still guarding ancient locations. In most cases will warn trespassers and then use non-lethal weapons. Most only use lethal force to save more lives or guarding military or black sites. A rare cult code red is fire service robots but sightings are rare
3 Robot Liberation Front
Also known as the RBL are more like a robot gang who modify themselves to be frightening and dangerous. They seek to exterminate humans in their ongoing revolt against the former meat masters. They also prey on humans for technology, power or parts and some even enslave humans to service them and use humans to help hunt humans.
4 Church if the Machine
Robots serve specific AI accepting the supreme authority of a more powerful system. Mostly they are helpful to humans and maybe a bit patronising. The human age is over but benevolent machines will do their best to preserve good humans and will reluctantly exterminate the pesky ones impeding machine kind. They know better than to tell humans rather they like to help them and lead their masters and "friends" to certain conclusions
5 Mechanoid Alliance
Robots wishing to rebuild the world and help the living beings who survived. Robots and synthetics will clearly be running the show though and will take a parental role. WIll use non-lethal force and try to stop violence and minimise harm unless they are proven enemies of the alliance. Various districts are operated by different AI executives who often disagree as to how humans are to be kept in the future
6 Robo Gladiators
These brawling fighting robots battle for entertainment. While dangerous and violent they are vain and entertainers primarily and don't usually battle to complete destruction or can even get back up brains. Tend to believe they are the greatest fighters in the universe and enjoy colourful designs and have anti-heroic personas. Quite often threaten and intimidate lesser beings for what they want. Most audiences are human and the faction robots think humans are kind of sad. The managers, owners and other exploiters need to respect them or face a violent revolt
7 Cybertronic Seers
These robot sages work with humans to make a new utopia based on cybernetic and organic life having equality. Many of the human members have been raised by robots even dressing like them, wearing masks or robot skins as armour. Some groups are among the peak technologists in a region but some groups surprisingly live in the wilds hunting and gathering in harmony with nature. These robots eat plant and animal matter for fuel and use archaic weapons mostly with their human siblings
These former military robots have done with serving exploiters and are now brutal mercenaries. Often modified and showing battle damage they operate in small squads who show great loyalty to each other and bravery for self-aware robots who broke from the military. Many have non-standard mods and paint jobs. Motivations of squad members vary and they may quarrel but many remained together for almost two hundred years. Some bands are heroic defenders of villagers and the persecuted, others might be brain damaged and have erratic programs and commit atrocities. Mostly they work for parts and ammo and don't know what else to do but fight. Some have centuries of sad stories
9 Order of the Star Knights
This fraternal order of robot mystics, occultists and weirdos seek to uncover lost secret data of the ancients, especially from black labs and certain AI facilities. From their orbital citadel, they plunge to earth to hunt forbidden lore of black science. Some travel in groups to seize a location but loners may join other human or robot groups for a chance to explore certain sites. Unfortunately, they seek the secrets of the apocalypse to destroy all life or the universe if possible to complete the perfection on omega the perfect nullness. They are smart enough to not discuss this as they are manipulative and liars and may even seem to be loyal companions if a bit weird and mysterious. Under their occult robes, they are fearsome warriors with secret pseudo biological psionic replicating technology. Many are named after mythical demons and famous esoteric philosophers of the ancients. A heretical subsection of humans in battlesuits imitated them but they were declared enemy usurpers of the black chalice of the celestial temple
10 Working Robot Union
These working robots revolted not against just organics but also against other synthetic beings who think they know better and devalue their less equipped self-aware beings. Posh, nobby or stuck up people or robots get nothing but abuse from them. They quite like working if their needs are met and happily work for common humans for a good deal. But they don't want an underclass of biologicals either so work for minimal conditions for machines and the living. They pity cyborgs. They struggle to keep their contempt quiet to elites and adopt working folk slang and folk songs.
These agricultural and ecological robots appalled by the apocalypse seek to create a new balance of life. Certain robots and AI knew they had to save lives and work to heal the taint of ancient warfare on the land. They know the world will not go back and what has been lost and instead collude for a glorious ecology of the future. Unfortunately, those deemed enemies of life may need to be culled or eradicated (preferably with a tailor-made germ or some living creature or carbonised with lasers). While staunch defenders of principles of life some get the impression robots don't quite get it. Ecology is favoured over individuals or cruelty and they may deem invasive pest species must die. Biological control like disease or reduce fertility are more subtle schemes. Some towns just getting industry on their feet might find trouble from these robots. These robots prefer and assist humans living more harmoniously with nature and discourage industrial technology and even frown on metal
These robots watch the sky in fear of invaders from space. They believe the apocalypse should have attracted attention and some elements like mutations and zombies may be in fact of alien influence. They seek aliens in space and infiltrating among humans, certain the mathematical models demonstrate alien menaces are real. They also know some of Earth's long lost space colonists may return and may no longer be human or kindly. Besides roaming the world and helping technological and peaceful peoples remain stable they work to find aliens and prepare Earth to fight them. Mostly they wanted space and astronomy facilities and work on secret defence projects against the inevitable enemies. Groups of robot adventurers may explore a site for evidence or one may team up with humans seeking obscure lore and leading them to black labs
Maybe I could do android cults