Nothing. It's all yours.
Your reading history cannot be seen by anyone but you, and it is important to emphasize that Reading Queue does NOT operate any database server of its own.
Your queue and archive are backed up and synced across all your iPhone, iPad and Mac devices where Reading Queue is installed. All your data is stored on your PRIVATE iCloud storage, which means that ONLY YOU can access them. You can turn this feature off and erase all Reading Queue data from your private iCloud storage at any time.
Reading Queue for iOS was using Google Analytics for Firebase until version 1.5, where it was removed.
The Reading Queue browser extensions for Safari, Firefox and Chrome do not use or inject any kind of tracking script. They just communicate securely with Apple's CloudKit web services.