Is it necessary to make up for (qada') or offer expiation (fidyah) in the event of doubt regarding not having fasted a debt from a previous Ramadan, and what is the value of the expiation if it is obligatory?

As long as you are unsure about making up the days you owe, the default is that you are accountable for them and must make them up. This is because whoever doubts whether they have performed an obligation, the default is that they have not performed it. However, if you are prone to many doubts, reaching the point of obsessive thoughts (waswasa), then you should not pay attention to this doubt. If it is obligatory for you to make up these days, then no expiation (fidyah) is required of you, because forgetfulness is an excuse that waives it.