We are obliged to believe our conscience, and ultimately be judged after our death on it. Conscience is an ordinance of reason. According to "Liberalism is a Sin", reason enlightened by faith is a true "authority".
People who believe Leo XIV is a true pope have necessary moral obligations. They MUST submit to him and his hierarchy, meaning the bishops under him, and the parish priests under them. That is the way God designed His divine Church.
God gave us the use of reason for a reason, reason enlightened by faith is our guide to know right from wrong, good from evil, so that we always do what is right and turn away from all that is evil. This is the authority that our conscience has over each us - and only over each us, individually, and only as long as we do not ignore it. In a nutshell, this is the extent of the authority you mention above.
God does not permit us to blindly submit to anyone on this earth while we live, not even to popes, not even to saints and angels (Gal.1:8,9). To say that we MUST submit to him and his hierarchy wholly disregards the highest of all the principles in the Church which we are bound to employ in all circuмstances of life until our last breath: "
We are first of all under obedience to God, and only then under obedience to man" - Fr. Hesse