I finally figured it out.
The problem was that when I imported Touch Camera PRO into my project, Lean Touch input manager (https://assetstore.unity.com/packages/tools/input-management/lean-touch-30111) was also already present - as I am in an experimental phase to find the most suitable solution for my project.
So as a result very strange things happened, the Components of the two packages started to mix together on the Game Objects. These two packages have Components with the same names, but in different namespaces, so I don't really understand how, and exactly what happened, but somehow same named Components appeared on the TouchCameraInputs Game Object from the other package too. Plane Game Object in the scene was getting the Plane Component from the other package, so CameraSideScrollOrtho Component lost the reference of the right Plane.
So it was a confusion between two similar packages....
I am not sure if any action should take place to help people to avoid falling to a situation like this, maybe indicate this risk in the description in the Asset Store, or maybe it is just an edge case comes once a year for hundreds of users, or maybe it was my fault as I should know that multiple input manager packages should not be installed at the same time.
After all I learned it well thats for sure... 🙂
Thank you for the helpfulness!