It doesn't. It does create a 3rd table. ArcGIS creates a wide variety of tables in its databases that it does not expose to the user in the user interface of ArcMap or ArcGIS Pro. The additional table for a relationship class is just one of them.
The documentation for creating a relationship class explicitly states:
For many-to-many relationship classes, ...
You need to do ctrl+shift+v and in the opening dialog, select database. Then select proper source and type for the database. Esri database is one of the options and select new connection. Point to the directory which contains your desired DB, and OK. Now you're ready to go.
To read a table in a geodatabase to a NumPy Array you can use arcpy.da.TableToNumPyArray(in_table, field_names). Specifying a list of field names is recommended for performance reasons, but you can use '*' for all fields. The resulting NumPy Array can be converted to a Pandas DataFrame.
import pandas as pd
input = r'my_project.gdb\my_table'
It sounds like the projection is missing. You can set the projection using Assign projection tool
...creates a new layer with the exact same features and geometries as
the input one, but assigned to a new CRS. The geometries are not
reprojected, they are just assigned to a different CRS.
This algorithm can be used to repair layers which have been assigned