What is the ruling on doubting backbiting and the actions that result from it?

The fundamental principle is the presumption of innocence (bara’at al-dhimma). Backbiting (gheeba) is your mention of your brother with what he dislikes. Therefore, backbiting is dependent on an utterance and not merely on suspicion. Suspicion does not entail a ruling nor does it necessitate anything. It is advised to stay away from delusions and doubts, because their abundance is among the steps of Satan that cause a servant to fall into whisperings (waswas).