post 2.5 releases have this pre-installed according to the dosumentation.
I would open up your anaconda prompt and use:
conda install -c esri arcgis
All the info should be here:
You guess it didn't work? Either it installs or it doesn't, there isn't any guessing. When you ran that command, what did the output say?
Are you running the Jupyter Notebook through the conda that is packaged/deployed with Pro, or is this a separate conda installation?
The screenshot shows the opposite, i.e., the screenshot shows a separate conda installation because ArcGIS Pro does not install its conda into C:\ProgramData\Anaconda. The directory being shown is the default location for an Anaconda distribution installed at the machine level for all users. The error message is stating the user running the command doesn't have proper permissions to install new packages.
It failed... that is why you don't have arcgis, you don't have permissions to install it.
I suggest that you only play with the arcgis module if you have a current version of arcgis pro installed and... you have created a clone into which you can install arcgis as well. Arcgis is installed in the base environment of Arcgis Pro since at least 2.5. Jupyter is also installed