The amount of trolls in this thread that either try to spew false information intentionally or just have no idea what they are talking about is insane.
If you are worried about what data (including your phone number) law enforcement can recieve (if they have your specific user ID, which is not equal to your phone number) from the Signal company check this: https://propertyofthepeople.org/document-detail/?doc-id=21114562 Tldr: It’s the date of registration and last time user was seen online. No other information, Signal just doesn’t have any other and this is by design.
If you want to know more about how they accomplish that feat you can check out the sealed sender feature: https://nerdschalk.com/what-is-sealed-sender-in-signal-and-should-you-enable-it/
or the private contact discovery system: https://signal.org/blog/private-contact-discovery/
Also as Signal only requires a valid phone number for registration you might try some of these methods (not sure if they still work): https://theintercept.com/2024/07/16/signal-app-privacy-phone-number/
There definitely an actively developped open source privacy focused period tracker available, go check it out: https://gitlab.com/bloodyhealth/drip But all data stays local on your device , which is of course good from privacy pov but if you are looking for something accessible from different devices then this might not be suitable.