ArcGIS Linux runs arcpy using wine [1]. Python is a simple wrapper in bash.

Step by step guide

1. /arcgis/server/tools/python

Python3 via Wine cmd

See [2] for running conda like Windows environment.

1. $. /arcgis/server/framework/etc/arcenv
2. $wine cmd
3. cd c:\Program Files\ArcGIS\Server\framework\runtime\ArcGIS\bin\Python\Scripts
4. conda create --clone arcgispro-py3 --prefix "Z:\home\arcgis\bin\Python\envs\test"
5. proswap Z:\home\arcgis\bin\Python\envs\test
6. conda install pyarrow
   1. This will install packages under Z:\home\arcgis\bin\Python\envs\test
7. Run python and test import.

Python3 via Wine only

1. Set up path for wine.
2. Execute python3 under wine.
3. Alternatively, you can run python in custom environment.

Note: ArcGIS Python doesn't include GDAL but it has many APIs [3].

References

1. Running Windows Batch Files on Linux
2. Deploy custom Python packages for ArcGIS Server
3. ArcGIS Pro: Raster Object