How can I run this SQL query across all of my databases at once?
The easiest way is to create a registered server group in Management Studio, add the server registrations you want, then right-click the group and select "New Query." The query you run will be run against all of the servers (with an additional leading column that indicates which registration it came from):


  


Of course this relies on all of the servers in the group being alive and reachable.

Some other approaches include Central Management Servers (here are official docs on that) and PowerShell (here's a blog post from Jonathan Kehayias showing how to run a query against all of the servers listed in a text file).