At least, doing the goof of reusing the OTP makes one vulnerable to disclosure of any of the key, which trivially reveals all the others.
For the rest, the consequences depends heavilly on what the keys are intended for. If the keys are intended for a block cipher that is secure including under related-key attack (as AES almost is), then there is not consequence beyond the aforementioned.
But in other cases the goof can be damaging, even disastrous. Simple example of the worse: the two random keys enciphered under two-times Pad are really random half-keys, intended to be held separately and combined by XOR to form a full key when needed (which is a simple and most common form of secret sharing with 2-out-of-2 parameterization); with the goof, the full key is the XOR of the ciphertexts for the two half-keys, thus is compromised, even though the individual half-keys remain confidential.
There is a spectrum in-between if the keys are for ciphers with poor security, especially under related-key attacks. In particular, if there are many keys enciphered under many-times pad, the goof allows the attacker to effortlessly pinpoint a key pair with much lower Hamming distance than average, and that pair might become the basis of a cryptanalysis (e.g. from ciphertexts for known plaintexts enciphered under both keys).