Do I need to visit all of the SE sites everyday that I want to obtain the Enthusiast, consecutive days badge for? Or does interacting with just one count for all of them?
Just based on the wording of your question, I wanted to clarify... the
Enthusiast badge is separate for each site. If you visit Stack Overflow for 30 straight days you get the badge for Stack Overflow. Then if you visit Unix & Linux.SE for 30 straight days, you get the badge for that site. The badges are unique to each site.
If someone visited every SE site for 30 straight days, they either deserve a badge or a psychiatrist.