OK- I will try to help a little.
Your female is probably more upset than excited to have him in her cage.
Never put a brand new acquisition with an established uro-it could spread parasites and disease to your healthy one(s)if it is sick.
If you do end up housing them together, you will need to at least rearrange the cage with separate basking,hiding, and feeding spots-and put them in simultaneously-also clean everything and change the substrate-uros are territorial.But wait until he is healthy for sure.
Soaking will not rehydrate unless they drink.
Maybe the water perked him up due to the temp, or maybe he just wanted out.
A vet trip or at least a fecal test is a good idea- if you don't know what is wrong.
I cannot say why he would be lethargic-it could be any number of or combination of reasons.You DO have a common "petstore" question but there is no one answer.
I would set him up by himself and give him a wide range of temps from 80-110 air temps (70-77 night)with a surface temp on the basking spot (this is me, now, some will say higher and many will say lower) of let us say at least 125up to maybe 140 or so peak temp and see if he moves or eats. If he was kept too hot he may want it cooler:120-125 surface temp. If you can, create a hot spot surface gradient, the wider the better: say 115-145,remember if he was too hot he will likely stay away from the hotter temps, and be always be careful not to raise the air temp too high. Test his poo and treat accordingly. Leave him alone(don't look at him all day, handle him as little as you possibly can,i.e. only for treatment).And give him some time to adjust. Find a quiet place for him and see how he does. I don't know if you have access to a good reptile vet that knows uros-if you do and you can, then go.(but test that poo).
Feed him a staple diet-endive, escarole, dandelions(if there are any dandelions left in the store-i haven't seen any since summer)raddiccio often comes pre-packaged with the first two I mentioned and is good mixed in with the other staples as well.
You can drop some water on his snout to see if he drinks or you can offer a water dish for a few hours a day.
Like i said common question, common problem, no one answer. I asked ,too. I have done it, I have made mistakes, hope I helped you as others helped me. I find the hotter surface temps keeps them moving and eating,and therefore growing and gaining weight.BUT in a small enclosure, or any enclosure for that matter, when you have high surface temps be careful not to let the air get too hot. Good luck w/ your Mali's. If I missed anything I'm sure someone will add it, or offer a different suggestion.