Upon initial server/docker setup for my Rust server, the necessary folders are created and I can begin installing plugins and everything works as expected. However, when restarting the server via RCON/console or restarting the docker outright, uMod/Oxide is not loaded at all. Is there a console command available for checking and running uMod/Oxide?

You should always load oxide again after running steam update.    oxide.version  Check if the command is installed by typing