Signing in to the backpack and connecting via the API will take different code paths, so being able to sign in to the website doesn't indicate the problem is with Moodle. The error you showed is definitely part of Persona's code, and the fact that there are other reported errors with the same message make me strongly suspect it is a persona issue.
I'm not able to reproduce the same issue on my Moodle Cloud account (though I don't have access to IE to test).
So at this stage I think my advice of contacting Mozilla is still the best course of action. Any other information you can provide may help though, for example:
- Exact version of moodle, and server details such as database, server type
- Whether the issue happens for you in other browsers
- Debugging information on network activity during the connection attempt. This will require opening the developer tools and looking for errors on the console and finding and exporting information about requests. I'm not familiar with how to do that in IE so can't really advise further.
Simon