This is a frame challenge. You have been warned.
There are loads of interesting stories around uplift, but most of them don't seem to ask the Malcolm Question: should we? Uplifted chimps or dolphins are just presented as a fait acompli, now we have to deal with the fallout. You seem to be in a similar situation.
The answer you're looking for is probably bound up in the answer to an earlier question: why did we uplift them? If our ethical standard had already evolved to the point where we've already granted them all of the same rights as humans then what reason would we have to violate their species identity without their informed consent?
Well, because we could of course! Shut up Dr Malcolm, we've already done it. You're too late as usual. Yes, your hindsight is incredibly acute, but it's not useful.
Where was I? Oh yes...
Given that champanzees are equivalent to humans by your legal structure, uplift is an illegal pursuit. You'd break huge amounts of laws against kidnapping, medical testing, performing medical procedures without informed consent, genetic modification without consent, eugenics... the list goes on and on. And on.
But it has apparently been done. That means that you have a completely unethical bio-science group who don't care at all about silly things like ethical or legal constraints. What makes you think that these poor citizens, after being illegally modified by a crazed group of evil geniuses, would ever be released from their cells? I don't think you thought that through.
But let's introduce an external factor who free these poor unfortunates from their captivity. What happens next? Let's say we have a group of illegally modified non-human sapients whose genetic material has been extensively modified. They can't survive in the wild with their cousins, and in fact their altered appearance makes it certain that they'd be killed if you tried. They're now smart enough that they can tell you exactly how miserable the idea of living in the wild makes them too. The only viable options they have is to form their own little community.
So they get legal representation, sue the company and the mad scientists - or their estates, depending on how the rescue went - that created them and now they're moderately wealthy. They're a tiny community of highly modified sapient creatures, with no social skills and an average lifespan around 40 years. Unless there are enough of them with high enough genetic diversity the group dies out in a few generations. And since they're smart enough to figure that out the suicide rate is going to be ridiculous.
Too dark? You said they had human rights. What did you expect that to mean?
OK, let's assume that human rights aren't extended to creatures we might want to uplift, like chimps and dolphins. And dogs, because doggos. We've hashed it out and decided that it'd be too cool not to have uplifted doggos, so let's do it! (While carefully not looking at the mountains of corpses from failed experiments. Go go Magic Biotech!)
Now we have dogs with human-level intelligence and a few physical alterations: hands capable of full manipulation, mouths modified to allow complex speech, that sort of thing. What do you do with them?
Well, first you give them a place to live. A community. You socialize them with each other and with humans, letting them figure out for themselves what their society is going to look like. They're not humans with fur after all, they're full sapients with all the rights - and responsibilities - that entails. You educate them, give them options for all of the training they might want, and eventually you have a proper uplifted species.
At that point the question of "what do we do with them" answers itself. You do nothing. They're smart, they have abilities that people will be interested in hiring (assuming you didn't modify their senses too much) and they can make their own way. They'll need financial support for a few generations, but who doesn't these days?
The same will be true of any uplifted species. If the reason for uplift isn't to make them better workers worth exploiting then you're going to have to put in a lot of work. And since they're not human they're going to come up with their own ideas about what a society of uplifted chimps or dogs or dolphins or whatever looks like. They might even have their own religions.
Oh, but be careful how smart you make them. A species of hyper-intelligent neo-chimps might sound like fun, but if they decide that humans aren't necessary anymore then they might be a little hard to stop. But don't make them too dumb either, because that's just manufacturing a low-intellect slave class. Hopefully we can tune it to human average, because clearly humans are the best example for uplift... right?