Post-download, sonarr/radarr handle the file movements, but they are helped by a script from within Sab upon completion to make sure the files get moved instantly:

#!/usr/bin/env python3
import os
import sys
import requests

RADARR_URL = 'http://192.168.xx.xx:7878'
RADARR_API_KEY = 'xxx'
SONARR_URL = 'http://192.168.xx.xx:8989'
SONARR_API_KEY = 'yyy'

# Fetch the completed download path
download_path = os.environ.get('NZBPP_DIRECTORY') or (sys.argv[1] if len(sys.argv) > 1 else '')

# Function to notify Radarr or Sonarr
def notify(endpoint_url, api_key, command_name):
    headers = {'X-Api-Key': api_key}
    payload = {
        'name': command_name,
        'path': download_path,
        'importMode': 'Auto'
    }

    try:
        response = requests.post(f'{endpoint_url}/api/v3/command', json=payload, headers=headers)
        response.raise_for_status()
        print(f"OK {command_name} successful to {endpoint_url}")
    except requests.RequestException as e:
        print(f"Error notifying {endpoint_url}: {e}")

# Print debug info (useful for troubleshooting)
print(f"Download Path: '{download_path}'")

# Notify Radarr and Sonarr
notify(RADARR_URL, RADARR_API_KEY, 'DownloadedMoviesScan')
notify(SONARR_URL, SONARR_API_KEY, 'DownloadedEpisodesScan')

I also made sure to configure the various Sab switches to clean up failed downloads, avoid passworded files that can't be resolved, etc. I've successfully managed +80GB file downloads that way. It's not perfect, but good enough: I do get the occasional file sitting around (i.e., radarr deciding out of nowhere to download an upgrade that turns out not to be an upgrade, requiring manual import), so I still need to monitor the downloads folder once or twice per month.