Tried this out today on Firefox and also saw the "This Kagi Privacy Pass token has already been used. Try turning Privacy Pass off and on again, or check our Privacy Pass documentation for troubleshooting tips" initially on most kagi.com page loads. Restarting the browser fixed that in non-private-browsing,but private browsing was still sporadically showing the same error.
Unfortunately after that the extension started getting stuck on the internal redirector page's .fetch
call on most requests. Looking at the console revealed that it was trying to access the .onion version of Kagi in the subrequest. I think this problem may have started after I tried out the .onion page in a container tab with proxy set to local tor. I had to disable the extension at this point.
To end on a positive note, this is a great feature to have when the issues are ironed out.
edit: Firefox 128.7.0esr, the version shipped by Debian.