Does the "identity" permission trigger a warning in a chrome extension?

Question

I've added the "identity" permission to my extension to implement a "Continue with Google" feature, but I'm unsure if it will trigger a new warning. If it does, my extension will be disabled for all users until they manually re-enable it by accepting the new permission, which I want to avoid.

I tried using Extension Update Testing Tool by Google, which is supposed to show what permission warnings are generated. It didn't show any new warnings after I added the "identity" permission. But the developer documentation states that this permission does generate a warning, specifically "Know your email address".

Screenshot of the relevant section in the documentation

Has anyone worked with this permission? Does it indeed produce a warning?

Also, I don't want to put this permission into "optional_permissions" because Firefox doesn't allow it there. Handling this differently on Chrome and Firefox would complicate the codebase, and I'd like to avoid that.