First, it is no problem to run a MultiBlocProvider to the screen and then have two BlocBuilders in parallel, e.g. one for each button or nest two BlocBuilders (which is essentially what .watch() would be if it is in another BlocBuilder).
But I have an opinionated answer as well. The two buttons will as you say run two separate processes, but I wouldn't separate them into two cubits as they are so tightly linked to the same feature and essentially the same state of that feature. I think a clean solution will be one cubit with separate methods, a HandleFirebaseVerificationCubit with a resendEmail()-method and a checkVerification()-method. Because I guess you'd want to either hide or disable buttons depending on a common state (e.g. NotVerified/Verified) etc.
I'd compare this to a form where you have a backend handling e.g. some validation which is triggered by a buttonpress and another button fetching some data to assist with populating textfields (e.g some address) You'd probably have one cubit for the entire form.