you can work around this by disabling "Always use private browsing mode"
https://guides.getalby.com/overall-guide/alby-browser-extension/faqs/can-i-use-alby-with-the-tor-browser
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11.5.6 (based on Mozilla Firefox 91.13.0esr) WORKS
12.0.3 BROKEN ted error occurred (Could not establish connection. Receiving end does not exist.) hello@getalby.com feedback
we look for beta testes for v12.0.3 - are you interested?