Period trackers are the perfect usecase for homomorphic encryption, where the system can operate on the data without knowing what the data says. It's slow and has a lot of overhead, but it's an active area of research. That way, the platform doesn't know what you're telling it. You have to trust the platform to have implemented it properly, and it's rather nerdy a detail, so it's no surprise there isn't one yet.

I love this stuff, even though its way over my head

> We are a community of researchers and developers interested in advancing Fully Homomorphic Encryption (FHE) and other secure computation techniques.

https://fhe.org/

(edit: formatting)