I worked on the design and rollout of multiple sign in providers on a popular app. There are best practices that avoid these issues (users forgetting which service they used), but they are rarely implemented.
The trick is to be very forgiving: If a user tries to sign in using provider X, and we discover an email address conflict with an account that uses provider Y, we would simply ask users to confirm by clicking a button to sign in with provider Y. From that point forward, both provider X and provider Y can be used to sign into the account.
So many apps miss the importance of this and cut corners by only allowing an account to be associated with 1 sign-in provider, or forcing users to create passwords for these accounts, or differentiating between login and signup.
The trick is to be very forgiving: If a user tries to sign in using provider X, and we discover an email address conflict with an account that uses provider Y, we would simply ask users to confirm by clicking a button to sign in with provider Y. From that point forward, both provider X and provider Y can be used to sign into the account.
So many apps miss the importance of this and cut corners by only allowing an account to be associated with 1 sign-in provider, or forcing users to create passwords for these accounts, or differentiating between login and signup.