I believe what you're looking for is Remote Path Mapping, read this guide and see if it fits your situation - https://trash-guides.info/Radarr/Radarr-remote-path-mapping/

Sonarr should be the same setup process. Essentially, you want your arr's to be able to see and access the files on your seedbox. Best way that I've found to do this is sshfs or rclone's sftp. Mount your seedbox's download folder on your Plex server with sshfs/sftp

Since you're also moving the files from your seedbox to your Plex server with synching, I imagine a setup involving mergerfs will work too. Basically, you mount your seedbox download folder to your Plex server, use mergerfs to merge it with your local Plex server's location that Sonarr/Radarr imports it to - point Sonarr, Radarr and the Plex to the merged location. When the files are being moved by Syncthing, all your services will still think they're in the same location so it doesn't get confused.

If you want to go that route, you can use the Google Drive guide - https://web.archive.org/web/20220508210909/https://wikiold.servarr.com/Cloud_Setup and change it a bit so it works for your configuration. Ignore the parts about encrypting and the nightly move script, Syncthing does that for you. And instead of mounting a Google drive remote, you will be mounting your seedbox through sshfs/sftp