I have achieved similar in the past with the below code. I have commented but let me know if anything needs clarification. Basically it uses a combination of the AGOLArcGIS Python API and ArcPy to access the feature services and export layers to feature classes in a gdb.
from arcgis import GIS
import arcpy
## set to True if you want any attachments to also be exported
## a lot faster to ignore any attachments if they are not needed as output
arcpy.env.maintainAttachments = False
## access AGOL
conn = GIS("home")
## you could change this to a list of feature service ids and iterate to
## export them to gdb
## get the item ID from the Feature Service page on AGOL, it is in the URL
## bar at the top of the browser
fs_id = "INSERT ITEM ID"
## gdb path to export to
out_gdb = r"INSERT GDB PATH"
## get the fs content, here is where you could loop through multiple feature
## service ids and export
item = conn.content.get(fs_id)
## use item.tables if interested in non-spatial tables
for lyr in item.layers:
## you might need to use the string replace function and replace any
## spaces with underscores as fc naming wont allow spaces and the
## feature class to feature class tool will fail.
fc_name = lyr.properties.name
## at this point you could use an if statement if you are only interested
## in layers with a certain name
print(fc_name)
## get direct url to the layer within the feature service
fc = lyr.url
## export to gdb
arcpy.FeatureClassToFeatureClass_conversion(fc, out_gdb, fc_name)
