In order to install the arcgis package in conda, you have to specify the architecture osx-64 otherwise the package will not be found. This works because MacOS will capable of running x86_64 code on Apple Silicon processors - that is how efficient they are!
conda install -c esri/osx-64 arcgis
In fact to make everything else work you need to add the channels with architecture specified exactly, e.g. conda-forge/osx-64, esri/osx-64 and defaults/osx-64. Otherwise packages will be installed with a mix of architectures and appears not to be able to find each other.