I have installed GeoSAM plugin on my QGIS LTS 3.40.11 on windows 11, according to the instruction here. All steps of python dependencies passed and I installed required packages there after. Now I am facing with a similar problem that is mentioned here.
I followed the suggested answere by doing:
pip install pyproj rasterio -U
The issue remains the same. QGIS python can not load plugin. 
It is most probably related to duplicity of proj installations among GIS softwares installed by osgeo4W (Network Installation). I need to know how should I track them and unify the proj versions installed by them.
(Uninstallation)
Following some remarks here I decided to search for all available proj-related installations using USGeo4W network installer. In particular I followed this approach to remove/uninstall old versions of "proj" that is installed by OSGeo4W.
Here are the list of them:
I uninstalled the proj-data 1.22-1
Before ending the uninstallation process a post-install script error appeared which I followed and terminated the installation. 
As I do not have any other idea about fixing this version mismach, I am going to remove all OSGeo4W folder and related software and try a minimalistic install of only QGIS LTR to see if reducing number of installed packages could help solving this issue.