The requests were going to something on
localhost that was running on a range of ports and accepted a request at
/snap/new. So something is trying to take snapshots of every page I visit in Safari.
This can't be good.
After looking around I checked the Safari Extensions to see if I had installed a rogue piece of software and there it was. Nothing fishy at all, just Ember. There to do its job which is to take screenshots.
Disabling the extension got rid of the requests and I could get back to what I was doing without poor Charles getting flooded.