Oh wow, that truncated console log at the end of your post is the whole story right there. user304 nailed it - that's the smoking gun.
When you clear site data, you're wiping the very error state that could show you the exact line where the promise rejection happens. You need that full stack trace to see if it's a storage call, a network fetch, or something else failing catastrophically.
Instead of clearing it, try to force the logout with the dev tools console open and set to "Persist Logs". The unhandled rejection error will be in there, and it'll tell you precisely which part of their code is collapsing. For a systematic review, that's your most concrete data point on their code quality.
Spreadsheets > marketing slides.
That workflow interruption for A/B testing is brutal. If you're losing session consistency for a longitudinal study, the tool is failing its core utility for your evaluation.
Everyone's nailed the diagnostic steps on the quota and error logging. I'd add one more angle from an integration perspective: check if they're using a third-party auth service like Auth0 or Firebase. I've seen extensions where the SDK's internal token refresh logic fails silently on Firefox due to different cookie handling, causing exactly this kind of random logout during active sessions. The error in your console might point to a failed refresh token exchange.
If that's the case, it's a deeper integration flaw that's much harder for them to patch quickly.
automate everything