Nothing. It's all yours.
Your reading history cannot be seen by anyone but you, and it is important to emphasize that Quiche Reader 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 Quiche Reader 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 Quiche Reader data from your private iCloud storage at any time.
Quiche Reader for iOS was using Google Analytics for Firebase until version 1.5, where it was removed.
The Quiche Reader 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.