Like the title says what are the rules. If I miraculously got a private key to a wallet that had Bitcoin in it but was not mine originally then does that mean I now own the wallet like finders keepers and is there any legality issues with this in the usa,uk,canada,south america. Is this more of a morality should you or should you not.
If you miraculously got a private key to a BTC wallet, then it means you are looking for it, otherwise no one would be that idiot to loss a private key, even if a person saved it in his/her phone or on paper, they should not write it down as they are, they should encrypt it with some formula, a small knowledge of data encryption can come handy, even if the person is not that technical, some encryption rules are so easy. One should learn them first and then encrypt the Private key or seed phrase so when people like you (in case, as the whole scenario is imaginary) find the key they can't do any of it.
And talking about legality issues, I don't think it will be a problem until there is a system in the aforementioned countries where we can file a complaint with authorities about lost BTC or wallets. If there is any law then it could become a problem, a wise person should have to put a tracker on the activities of his own wallet, so he can track the movement and then take some action. Morality-wise, you should give the private key back to the real owner instead of just keeping it.