I am MORE than happy to discuss robots and cyborgs in my setting, or really anything else. I guess since this is a really broad question I'll give a rundown of both in the context of the federal expanse specifically. It is effectively the 'federation' of the setting.

Robots have a wide variation in my setting. They can range from simple automatons with routine functions, to fully, legally sentient AI. I like to borrow the divide Mass Effect uses, VI & AI. Virtual Intelligence a system with fixed perimeters and Artificial Intelligence as anything that is considered adaptive or learning. That being said, not all AI are classified as legally sentient, certain traits have to be met to be considered fully autonomously sentient and given true citizen status. It's something similar to a turning test but can vary depending on extraneous circumstances. Sentient robots aren't particularly uncommon, but I wouldn't say they're common, either. Generally speaking, sentient AI and robots by extension, is a rather accepted concept.

Also this is more of the broad strokes of the idea, some planets and territories are much more restrictive to AI and what constitutes AI, than others. Wojciech for example, even though he is classified sentient by the federal expanse, some planets or territories will not honor his classification even if they're part of the expanse, as each planet is allowed to govern this aspect in on their own accord. If he were to be in one of these places, they would regard him with the same rules and restrictions they apply to any other robotic hardware.

Cyborg in a legal context is a term used to refer to any person with a prosthetic that require direct nerve integration. Current technology permits for some pretty advanced prosthetic integration from simple limb replacements to complex limb replacements with touch and sensation, from synthetic organs to full body prosthetics. There is a classification and clearance system for different forms of prosthetics, from average performance to high and unnatural performance. Typically the average person will not be able to buy something beyond the level exceptional natural performance. Access to prosthetics that provide unnatural performance or hide weapons are typically locked to those with the right clearance or those that know how to buy through less official channels. Most of the restriction is on the parts themselves, but not on the operations. If you already have the questionably legal part in your hand, you can get it installed at any reputable hospital. But there's always a risk they could report it if they know what they're installing. Of course there's always going outside the expanse to get work done.

For full body cyborgs, there is a special unique Bio-Registry that they are required to participate in if they're in one of the territories belonging to the federal expanse. The Bio-Registry is a database that contains extensive physical, biological, and historical information about the body before it underwent the transplant process. This is accomplished in the form of an exhaustive physical and harvesting of any and all biological tissue samples. It's purpose is two fold - to provide any possible medical information there could be if there are complications with the brain or other remaining organs, and to prevent full body cyborgs from escaping criminal charges should that arise after the fact. It is of course, a highly controversial practice but still one largely regarded as necessary. Some places outside the federal expanse practice something similar, and some don't at all and many will travel outside the expanse to keep their privacy. R'Vindr was one of those that went outside the system to ensure his past was inaccessible.