I'm still not sure what library Studio is using but I suspect it's openssl. What version of openssl are you running? ($> openssl version)
You can list the ciphers with $> openssl list -cipher-algorithms
There's probably a ton of output from dumping the ssl handshake and it's not easy to read. I don't know why crypto libraries have to generate such unreadable output and don't get me started on the error messages. If it's what I suspect you should see something in there about "unable to negotiate cipher suite" or something like that. If it is there's no need to dig through the list of suites from each library. It already did it for you and is telling you it ain't there.
SOLVED After much investigation and thinking about previous run-ins with certs, my co-worker figured out that the element Stardog Studio has been looking for in the cert is the Subject Alternative Name field. Once he added that to our cert, Studio was able to connect. Thank you all for your troubleshooting help!
@borgendorf First, thanks for posting the resolution to your issue here. We're glad Studio is now working for you.
Second, I'm now curious about your browser. I saw that you were using Vivaldi; do you know what version of Chromium it was built from? As I understand it, the Chromium team has recently made Subject Alternative Name a requirement for SSL certificates (you can see the discussion here: Redirecting to Google Groups), so I'm curious how your browser worked with this field missing. Perhaps your browser allows you to override the requirement? Or perhaps Vivaldi has disabled the requirement or is using an older Chromium engine?
In any case, the fact above about Chromium and the Subject Alternative Name requirement likely explains why this was not working in Studio previously. Studio runs on Electron, which uses Chromium at its core, so any requirements regarding certificates in Chromium are also requirements in Studio (there are cases where Electron modifies Chromium, but that apparently isn't applicable here).