I think you may be missing something with your interpretation of the SABnzbd categories. To integrate SASBnzbd and Sonarr you need to have two different folders configured. The first folder is the location where SABnzbd is going to put a completed Sonarr download and is controlled by the category definition in SABnzbd. The second folder is the location of your media library where you want your files to ultimately reside (which I assume is your 3tb drive). The second location is used by Sonarr’s media management and it will monitor completed downloads in SABnzbd that match the category that belongs to it (you tell Sonarr the category as part of the “Settings/Download Cient” definition) and move them into the media library once it sees they are completed by SABnzbd. Sonarr use the category to figure out what download belongs to it vs. Radarr and learns where SABnzbd put the completed download from SABnzbd itself which is why you don’t configure that category folder in directly Sonarr.
In my case, I have these SABnzbd category folders in my home as {home}/sonarr_stage (category is sonarr) and {home}/radar_stage (category radarr). You don’t need to worry about the SSD filling up as Sonarr and Radarr will move these files to /mnt/3tb/ locations as soon as they see them completed.
On your 3tb drive you would set up /mnt/3tb/media/Movies (configured as a root folder in Radarr “Settings/Media Management”) and then set up /mnt/3tb/media/Sonarr (configured as a root folder in Sonarr “Settings/Media Management”). You can also setup naming criteria and other options on this setting page that control how Sonarr and Radarr will handle the media.
Using docker comes down to your computer literacy as it does add a layer of complication. Things such as upgrades and rolling back versions can be much simpler and docker will run quite seamlessly but the cost is the initial setup and extra configuration that is necessary when using virtual computing machines. I run everything inside of docker personally (SABnzbd, Sonarr, Radarr, Readarr, Flaresolverr, and Jacket) as well as a special docker container called Watchtower that runs once a day and upgrades all the other containers when a newer version is available so I am always running the latest.
When getting Sonarr to work with any download client you have to look at it as two separate tasks. The first task is how do you get Sonarr to communicate with the download client so it can tell it what to download and then monitor the progress of the download. The second task is to get Sonarr to manage completed downloads so they are integrated into your media library.
The first part is pretty straightforward, configure a category in SABnzbd and note the exact name you used for the category (you mentioned you used “tv” and I assume that you set the path for the “tv” category in SABnzbd as /home/greg/Videos/Complete). Now in Sonarr, you need to go into “Settings/Download Clients” and tell Sonarr how to talk to SABnzbd (this is where you tell it about the “tv” category, note my category below in my setup is called “sonarr” and is highlighted in yellow).
Once that is done Sonarr can send NZBs to download to SABnzbd and monitor their progress. Of note, you do not need to configure inside of Sonarr where SABnzbd is putting completed downloads as that information is passed to Sonarr automatically by SABnzbd when Sonarr queries the status of a download.
In order for Sonarr to retrieve a completed download you need to configure the “Settings/Media Management” page inside of Sonarr which tells Sonarr how to add content to your media library. This page is where you configure a “Root Folder” which is used when you add a new series to Sonarr as Sonarr will set the media library path for any series you add as {root folder}/{Series Name} (assuming you are using standard naming configuration). The root folder must already exist in your filesystem as Sonarr will not create it although Sonarr will create all the Series Folders underneath it automatically.
Step 1 : Configure a category in SABnzbd that will be used by Sonarr.
Step 2 : Configure Sonarr to talk to SABnzbd which is where you tell Sonarr about the category.
Step 3 : Configure Sonarr on how to handle completed media including the “Root Folder” of your media library.
Note that until you add a “Root Folder” in Step 3 above you cannot add a series to Sonarr.