There are a multitude of calendar apps, tho I know of none specifically for birthdays exclusively.
- Nextcloud AIO combined with Nextcloud Android app
- Radicale combined with DAVx⁵ Android app.
- Baikal combined with DAVx⁵ Android app
Those are the ones I know of that have an Android capable app. There may be others. Maybe others here will chime in with some options.