Is a person considered a disbeliever for being discontent with Allah's decree after missing one prayer, and what is the ruling on their continued shunning of people and refusal of imamate because of that?

The matter is easier than you imagine, for Allah’s mercy encompasses all things, and a sleeping person is not held accountable for their actions, nor is they sinful for what occurred, even the Prophet (peace be upon him) and his companions overslept and missed the Fajr prayer. What you are doing is a trick of Satan, and a sign of extremism and a lack of proper judgment. Abandon these reprehensible actions of isolating yourself from people, refusing to lead prayers, despair, and hopelessness, and live your life normally. This religion is easy, and no one will make the religion difficult except that it will overcome him. So beware of extremism and excessive scrupulousness, and abandon these destructive whispers.