Age Tokens
Not that they're interested in using it this way, but it wouldn't be impossible for your Auth provider to issue you a token (JWT?) that you can then paste into whatever platform wants to verify your age.
The token only contains proof that the bearer is over 18. Doesn't contain any identifying information. Auth provider don't know where you used it, Auth consumer knows what provider it came from but not who it was assigned to.
Combine that with rate limits (restrict how long tokens are valid, how many each user account can generate per day, how many times the consumer will accept the same key) and you're most of the way there! It won't entirely prevent a black market for them, but nothing can