The answer from @PolarisKnight worked beautifully for me. I wish I could upvote that answer; I'm making a StackOverflow account for the first time just to indicate my support as I do not have the reputation to do anything but answer this question.

I swap between Cursor version 0.50.7 and VSCode version 1.100.3. My remote host is running Rocky 9.5 (an open-source Linux distribution meant to be compatible with RedHat 9). It has glibc 2.34 and glibcxx 3.4.29, so the answers regarding versioning are irrelevant. As a first pass, killing the server did not work either.

I originally could not connect via SSH from within either Cursor or VSCode. To resolve this, I installed PUTTY, connected to the remote through that, and then ran $ sudo yum install tar. After that, I was able to connect to my remote through both Cursor and VSCode on those respective versions.