When you set the deep link scheme and host in the supabase deeplink plugin and in the android manifest you have to remember to set the additional redirect url in the subabase auth settings. E.g. if you have supacompose as your scheme and login as your host set this to the additional redirect url:

MainActivity

Note: you should probably use a viewmodel for suspending functions from the SupaCompose library

class MainActivity : AppCompatActivity() {

    val supabaseClient = createSupabaseClient {

        supabaseUrl = "your supabase url"
        supabaseKey = "your supabase key"

        install(Auth)
        install(DeepLinks) {
            scheme = "supacompose"
            host = "login"
        }
    }

    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        handleDeepLinks(supabaseClient) //if you don't call this function the library will throw an error when trying to authenticate with oauth
        setContent {
            MaterialTheme {
                val session by supabaseClient.auth.currentSession.collectAsState()
                println(session)
                val scope = rememberCoroutineScope()
                if (session != null) {
                    Box(contentAlignment = Alignment.Center, modifier = Modifier.fillMaxSize()) {
                        Text("Logged in as ${session?.user?.email}")
                    }
                } else {
                    Box(contentAlignment = Alignment.Center, modifier = Modifier.fillMaxSize()) {
                        var email by remember { mutableStateOf("") }
                        var password by remember { mutableStateOf("") }
                        Column {
                            TextField(email, { email = it }, placeholder = { Text("Email") })
                            TextField(
                                password,
                                { password = it },
                                placeholder = { Text("Password") },
                                visualTransformation = PasswordVisualTransformation()
                            )
                            Button(onClick = {
                                scope.launch {
                                    supabaseClient.auth.loginWith(Email) {
                                        this.email = email
                                        this.password = password
                                    }
                                }
                            }, modifier = Modifier.align(Alignment.CenterHorizontally)) {
                                Text("Login")
                            }
                            ProviderButton(
                                icon = {
                                    //  Icon(painterResource("discord_icon.svg"), "", modifier = Modifier.size(25.dp))
                                },
                                text = {
                                    Text("Log in with Discord")
                                },
                                modifier = Modifier.align(Alignment.CenterHorizontally)
                            ) {
                                scope.launch {
                                    supabaseClient.auth.loginWith(Discord, onFail = {
                                        when (it) {
                                            is AuthFail.Timeout -> {
                                                println("Timeout")
                                            }
                                            is AuthFail.Error -> {
                                                //log error
                                            }
                                        }
                                    })
                                }
                            }
                        }
                    }
                }
            }
        }
    }

}

AndroidManifest

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android" package="io.github.jan.supacompose.android">

    <uses-permission android:name="android.permission.INTERNET"/>

    <application
            android:allowBackup="false"
            android:supportsRtl="true"
            android:theme="@style/Theme.AppCompat.Light.NoActionBar">
        <activity android:name=".MainActivity" android:exported="true">
            <intent-filter>
                <action android:name="android.intent.action.MAIN"/>
                <category android:name="android.intent.category.LAUNCHER"/>
                <action android:name="android.intent.action.VIEW"/>
                <category android:name="android.intent.category.DEFAULT"/>
                <category android:name="android.intent.category.BROWSABLE"/>
                <!-- This is important for deeplinks. -->
                <data android:scheme="supacompose"
                      android:host="login"/>
            </intent-filter>
        </activity>
    </application>
</manifest>