Is the prayer of a man who intends to pray Asr behind someone praying a supererogatory prayer valid, taking into account that he intended to pray Asr while in doubt, and is it permissible to consider his prayer supererogatory if it is not an obligatory congregational prayer?

Your prayer behind someone performing a supererogatory prayer, with the intention of praying 'Asr, is valid, because it is permissible for someone performing an obligatory prayer to follow someone performing a supererogatory prayer. And hesitation in interrupting the prayer does not invalidate it as long as there is no firm intention to stop, based on the statement of Sheikh Ibn 'Uthaymeen: "As long as he has not firmly intended to stop, he remains upon his intention." So, as long as you did not become certain of the intention to stop, your prayer is valid and you are not required to repeat it.