It's known bug first seen in Firefox 86 for macOS. I reported it to Firefox developers, they working on fix.
The Raindrop.io browser extension does not completely function in Firefox’s private browsing mode. This is a known issue specific only to Firefox. We have discussed the problem with Mozilla, however, they seem unable to fix it so that extensions like Raindrop.io can function entirely in private mode.
Firefox Bugzilla report: https://bugzilla.mozilla.org/show_bug.cgi?id=1329304