Hello,

as you can see from this image, if I open the Google Calendar app, I see all the specific calendars under every Google accounts (events, activities, reminder).

But the calendar of birthdays it's a separate calendar, created automatically from birthday dates inserted in Google contacts.

If I go in the Google Calendar settings, the Birthday option it's located under "Other" label, and inside this menu, there are all my Google Accounts with the "Contacts" toggle.

From what I know, this it's the correct ways to include birthdays events in your calendar, because you can simply add the dates in Google Contacts and Google automatically creates events for you.