Question regarding multiple auth

Hi! 👋🏻 We're building a platform where users can log in from multiple platforms to pool the stats from each (YouTube, Twitch, etc etc) and were looking to add authentication to basically prove they are the specific users to pull the data from. Would I be right in saying that using Supabase auth wouldn't be the best way to handle this? The reason being that if the user was signed into our platform via an email that's different than the email on one of their social media accounts, because then they'd be separate users?

For example:

User signs up to our website with email@email.com and then tries to auth their twitch which has the email otheremail@email.com

Any thoughts or opinions on this would be super helpful! 🙏🏻
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