The waning crescent thing is pretty significant. People born under this phase are described in lunar astrology as old souls with heightened intuition and psychic abilities (is that sounding familiar?). It’s the final phase before the new moon, so there’s this quality of being between worlds - endings and beginnings. Between the 3D and the 5D.
Really, like any external sign for twin flames, this can only tell you so much. Even the moon phase calculator gives you a vague idea because knowing if someone is your twin flame is hard when you’re working entirely with external signs and confirmations.
What’s interesting, though, about both of you having it is that waning crescent people are said to be completing karmic cycles from previous lifetimes. They’re the wisdom keepers, the ones who can see in the dark when others can’t. The phase spans about 3.5 days, and being born just three days apart means you’re in nearly identical positions in that cycle.
Traditional astrology focuses more on moon signs and aspects rather than phases, but the birth moon phase does reveal how you process emotions and manifest your life purpose. The same phase suggests you both have similar instinctual responses and emotional rhythms. That means a deep understanding, but you also need things at the same time.