I wish I could be more helpful, but I have not yet figured out the best way to deal with Lightroom. Am I right in assuming you are on the Photography plan with Adobe — Photoshop, and LR?
LR Classic is the original LR before they introduced a Cloud version. It is a desktop version — meaning all your photos are only available on your computer. It looks like your CC settings kept that Classic 6, even though they are well past that now — currently v. 11.2. Unless you had some problems working with the newer versions, you don't need v. 6 — although I'm not sure if your v. 6 catalog is the same as what's used for the newer versions, so don't uninstall v. 6 until that is sorted out. Theoretically, if you open the most recent version of Classic, it should know — or ask you what catalog to use and you should be fine. Theoretically.
When LR CC was introduced, there was no additional cost for those on the Photography Plan. Obviously, the CC version makes photos available on your devices because they are stored in the Adobe cloud. Initially, there was no clear guidance on what to do if you were a Classic user and when I installed and opened LRCC on my iPad, it started importing ALL of the photos in the Apple iCloud into the Adobe cloud. Yikes — that number of photos would clearly exceed the free storage Adobe includes and I didn't want to pay for more, so I "paused" that import and somewhere found a setting to tell it not to automatically import.
So now I pick photos individually from my Apple iCloud photos and import them to LRCC when I want to work on them on my iPad. BUT to make matters worse and even more confusing, somehow I lost the catalog for LR Classic (not the photos, just the catalog with the keywords). LRCC is still sitting there empty on my iMac, waiting for me to figure out what to do, although LRCC on my iPad and some photos there.
To make things even more confusing, once Apple got so good at synching Photos across devices using their own cloud, I stopped importing photos to my iMac, so now I have over 16,000 photos in the iCloud that are not on my computer.
It's a really frustrating and confusing mess, and as (very) technical as I am, just the thought of sitting down and trying to think it through and researching the best way to do it is enough to make me curl up in a ball and cry.
See — I told you I couldn't be helpful. Lol.