Birthday Hub doesn’t collect and share any data with third parties. OneDrive is only used for the backup and restore of your data and to synchronize the by this app used data with your other devices which also have installed this app.
Some anonymized program informations may be sent to Microsoft (e. g. for error analysis if the app stops unexpected or crashes).
But I point out that software may have security gaps and errors. I can not guarantee that your data is fully protected in this app.