I can't see the pics but the video looked more like a rat than a squirrel to me, cant get a sense of scale tho.
If you're in the USA, rabies is a big concern but I looked it up cause I always heard squirrels can have rabies but apparently the CDC says small mammals are almost never found to be infected and are considered non-risk. (TIL!)
I have friends who have taken in baby wild animals as permanent pets such as wild rabbits. Very similar situation: found on the side of the road, assumed to be dying, fed with a pipette or syringe and made full recovery. But it's often down to luck, often they are kicked out of the nest/brood because they were terminally defective so don't feel too bad if they don't make it.
Wild rodents are different from domestic breeds, usually a bit more rowdy but still very much intelligent and trainable and affectionate. They adapt just fine to the cosy life if they are raised from a young age. Rats and Squirrels are very underrated pets IMO, they have so much wit and personality. They will need a lot more space and climbing equipment than a hamster though.