If AEM redirects to /saml_login after authentication instead of the intended page, check the following:

1. SAML Authentication Handler: Ensure the Default Redirect URL is set correctly in AEM (/system/console/configMgr).

2. Sling Authentication Service: Verify login selector settings (/system/console/configMgr/com.day.crx.security.auth.login.LoginSelectorHandler).

3. IDP Configuration: Ensure the RelayState parameter is correctly passed.

4. Dispatcher Cache: Make sure /saml_login is not cached.

Try these and let me know if the issue persists!