If you put that request in the repeater (in Burp), you can test with and without the double slash. See if you get a different response.
I personally doubt that the double slash is an issue. Maybe there's information in the response or its headers ?
Do you guys test with the preview branch of Sonarr? I can't get nzb360 to connect to my instance of Sonarr through Burp proxy anymore. I'm currently running Sonarr version 22.214.171.1241-ls38 by linuxserver.io. I don't have issues with other nzb apps like LunaSea. They all display episodes properly. Only this one has an issue.