First of all, our group assumes that Tongue of the Sun and Moon is similar to Tongues, and that both abilities produce an audible effect that mimics the function of language but does not replicate it. The rules are somewhat vague on what reaching out and touching another creature's ki entails, but this is the stated mechanism by which the monk can understand other languages and allow others to understand what the monk says.
Master of Intrigue states:
Additionally, you can unerringly mimic the speech patterns and accent of a creature that you hear speak for at least 1 minute, allowing you to pass yourself off as a native speaker of a particular land, provided that you know the language.
Could Tongue of the Sun and Moon fulfill the requirement that a mastermind know the language of the person whom they are listening to, given that the monk can "understand all spoken languages"? Could a Mastermind Monk pass themselves off as a native speaker of a tongue they don't actually know?
For context, our party faces regular language barrier challenges within an intrigue-heavy campaign. We have assumed that while understandable, the language produced by the Tongue of the Sun and Moon sounds noticeably distinct from common, or whatever other language a creature would expect to hear. As a consequence, a monk could not effectively impersonate someone who speaks a language they cannot speak, without their obviously garbled ki-enhanced gibberish blowing their cover.