How do I find out what app is showing a toast?
You could use the Toast Source app for that. It not only integrates the app icon and name with each toast message (first screenshot below), but also gives you a history of toasts you received and which app sent it:

 
Toast Source (source: Google Play; click images for larger variants)

Quite privacy friendly it doesn't even require the Internet permission (so no ads either). But as it uses accessibility services, it's unclear whether it will survice Googles current purge.