"New" cloud types: Can they be used as markers for climate change observations?
My answer is no. The reclassification of clouds is not affected by climate change. It is more of our understanding of how they work, formation mechanisms, etc. Cloud classification can generally be broken down into altitude and shape (cirrus-type, cumulus-type, and stratus-type). The subtypes of those describe the behavior, and may be combinations of types (such as cirrostratus, pyrocumulus and cumulonimbus). There are other types, such as the new asperitas cloud (formed by gravity waves), the Kelvin-Helmholtz instability cloud (formed by the Kelvin-Helmholtz instability), contrails (formed by jet exhaust), fog (formed by either advection or radiation), etc.

That is not to say that clouds don't affect climate. For example, cirrus clouds, and other high clouds, are optically thick, preventing the low temperature from dropping. It has been debated what the net effect clouds have on the environment, newer research seems to indicate net warming (see latest IPCC report), despite the traditional thought being cooling. Being that water vapor is a greenhouse gas with generally greater concentrations than the famed CO$_2$, it is extremely important to consider in climate discussion.