[deleted]
Looks like it depends on where you are saving the contact to.
Just tested it on my GOS with the built-in Contacts app and if directed to "Saving to Device", hitting "more fields" doesn't reveal such a field but "Saving to "DAVx5 Address Book" (this is what I set/use) has it.

    2 months later

    When importing the .vcf file, birthdays are kept.
    Unfortunately the birthday date field is missing in the Contacts app. Don't know if pictures profile are kept also (probably not).
    The Simple Calendar app is able to import birthdays from contacts (but can't save new dates for contacts)

    25 days later

    With every android phone I have ever used, no matter Samsung, Motorola, Google, etc they all have a birthday field under each contact, not Graphene. Why is this? It's incredibly important for syncing calendar events, reminders, etc. Can this be fixed and added to the bug list? And please, let's not call this a "feature" - every contact has a phone number because you need to communicate with them, just like every contact was born. It's a bug.

      graphite-or-graphene all have a birthday field under each contact, not Graphene

      This has already been answered in this thread. Its not the contacts application or the operating system, its the capabilities of the storage backend. With other Android, you are probably using the google account contacts backend by default. With GrapheneOS, your default will be "on device" which has limited capabilities, but you can use a different storage backend like DAVx5 for additional capabilities.

        2 years later

        You can install "Fossify Contacts" from F-Droid which will allow you to view and edit the birthday.