I'd like to add this scenario actually happened during the Cold War. Soviets were reusing one time pads and the US army decrypted some of the messages, among other things this lead to discovery of Soviet spies targeting the US nuclear weapon program https://en.wikipedia.org/wiki/Venona_project
If you use the same one time pad to encode two or more different messages, then all the sorts of attack proposed here become plausible again.
The security provided by a one time pad relies entirely on the fact that it is only ever used once.