Here are my notes on getting Supabase working with Unity.
If you are only interested in using Supabase with your project with email/password accounts, it's pretty easy. The main thing is to use the Unity NuGet package to install UniTask (async/await) and supabase-csharp.
However, the really neat part is also supporting native Sign in With Apple on iOS. Apple is increasingly requiring developers to support Sign in with Apple on iOS, and it does provide a pretty seamless experience. One nice thing is that by following these steps Supabase integrates both the on-device native Sign in with Apple and the web-based version of Sign in with Apple. This means you could do something like having a iOS Unity project for your main gameplay or application, and also allow users to use the same account to access details in a web application (e.g. something you build in SvelteKit or React or whatever).
I'm assuming you want to support Sign in with Apple, so I'm providing the steps in the order I wou