I have the exact same question as posted at Attributing distance from feature in attribute table using QGIS, but for ArcGIS Pro.
I would like to create a field in the point shapefile attribute table which would be each point's distance from the coastline polygon shapefile.
I think you should try using the Near (Analysis) tool which:
Calculates distance and additional proximity information between the input features and the closest feature in another layer or feature class.
I do not think that will require you to convert your coastline polygons to lines first.
