Using the python request module and the official Synology documentation:

https://global.download.synology.com/download/Document/Software/DeveloperGuide/Package/FileStation/All/enu/Synology_File_Station_API_Guide.pdf

I have successfully retrieved API information, logged in, and requested for the File Station API. I've included my current code below:

import requests

if __name__ == '__main__':
    # Retrieve API Information
    response = requests.get("https://myds.com:port/webapi/query.cgi?api=SYNO.API.Info&version=1&method=query&query=SYNO.API.Auth,SYNO.FileStation.List")
    print(response.json())

    # login
    response = requests.get("https://myds.com:port/webapi/auth.cgi?api=SYNO.API.Auth&version=2&method=login&account="+str(user)+ 
        "&passwd="+str(password)+"&session=FileStation&format=sid")
    print(response.json())
    sid = (response.json()['data']['sid'])

    # request File Station API
    response = requests.get("https://myds.com:port/webapi/entry.cgi/?api=SYNO.FileStation.List&version=2&method=list_share&_sid="+sid)
    print(response.json())

    # logout
    requests.get("https://myds.com:port/webapi/auth.cgi?api=SYNO.API.Auth&version=6&method=logout&session=FileStation")

Doing this I can view the folders in the NAS, and looking at the Synology documentation I can download a specified folder or file within the drive with SYNO.FileStation.Download.

What I am wondering is there a way to use python to traverse subfolders within the drive and only download certain files (say based off of filename). I can't just download the main folder and then traverse it on my local machine (for example using the python OS module and the os.listdir() method) because it is extremely large so I need to do it through the APIs.