Hi! highway=busway is still a quite new tag, so it is not taken into use by all consumers yet. That not a good reason not to use it.
But there is other reasons «highway=tertiary» + «motor_vehicle=no» + «bus=yes» might be a better fit here.
«highway=busway» was conceived as a way to tag roads that are part of a «bus rapid transit» system (BRT).
It not enough that a road is bus-only, and there is no BRT-systems in Oslo.
Moreover, this road is not a bus-only all the time, its open for car traffic when Ekebergtunnelen is closed as a detour route.