First off, TLS is crypto bread-and-butter that's used for a lot more than HTTPS. You're not out of the woods because you're not running a webserver.
Second, SSH itself doesn't use TLS; it has its own protocol, so sshd isn't vulnerable.
But third, read overflows like this can be escalated in countless ways to total compromise if some credential, key, canary, or such gets leaked. So just because sshd isn't vulnerable doesn't mean you're not screwed.
Not only HTTPS. Many other protocols are TLS-based: modern email, some VPNs, etc. Really almost everything secret on the Internet is protected by TLS; SSH is a rare exception.
I am having a lot of trouble figuring out what you were attempting to convey in the first four sentences in your comment.
The one thing that I can discern is that you printed a list of every package that depends on libssl1.0.0 for your configured repositories. But you have no idea if those programs make use of heartbeat. ssh (and everything related like libpam-ssh) is on that list and does not use TLS. The same can be said for many others such as tpm-tools, ntp/ntpdate/openntpd, xca and so on.
