APM Cookbook: AutoLaunch SAML Resources
Marvin, when doing SP initiated, the auth request already identifies what app to redirect the user to and that happens natively, so the solution is not relevant for SP initiated problems.
As for your question about automatically sending SAML responses to every SP upon an SP initiated auth to any one of them (or for that matter, upon launching the webtop for IdP initiated), it's not something most environments would want but you may have a good use case. Theoretically it's possible, you could use this as example code to start from, and you'd have to make sure you launch a new tab for every one of those SPs. It would be definitely solving a different problem than this code, so I'd suggest that this work should happen/be published under a new article. If you take it on, be sure to comment back here linking to your new article so we can see the great solution! As you build that solution, remember that when publishing apps on a webtop for IdP initiated, SP initiated also automatically works in that same deployment.