You won't be able to do it from inside Calculate Field. In Arcade there's no way to get the shape file's path, maaaybe you could do it with Python (I doubt it), but that would be complicated.
This is a job for a simple Python script. Edit the script and execute it in the Python Window, in a Notebook, or in your IDE:
import arcpy
from pathlib import Path
# get a list of your shape files
# if they are in different sub folders, use rglob instead of glob
folder = Path(r"H:\Test")
shape_files = folder.glob("*.shp")
# go through the list and calculate the field for each shape file
for shape_file in shape_files:
shape_file = str(shape_file) # CalculateField is old and can't handle Path objects...
print(f"Adding field to {shape_file}")
arcpy.management.CalculateField(
in_table=shape_file,
field="OrigPath", # shape file, so can only be 10 characters
expression=f"'{shape_file}'" # this is a string argument, but we also want to return a string, so we use single quotes inside the expression
)
Have a great day!
Johannes