One of the “hot” areas of atmospheric research these days is in the study of the phenomena of ice supersaturation. Ice supersaturation is when the relative humidity with respect to ice in the atmosphere exceeds 100%. Under these conditions, the sky is clear with no clouds.
Cirrus clouds in the upper troposphere have only a loose relation to ice saturation. They do not typically form at saturation and once formed they are not very strongly attracted by the equilibrium state. Thus, there is plenty of ice supersaturated, yet clear air in the upper troposphere.
Google the term ice supersaturation
and you will find hundreds of research papers by scientists from all over the globe studying this phenomena.