I’ve never heard it talked about since I started getting involved.
But I’ve noticed it being referenced in a couple obscure places.
The most recent example being our Code of Conduct,
which references this file in the repo.
The contents of the two don’t actually match,
The content in the website-copy repo seems to be out of date.
The commit history shows the repo is used for mentor notes, auto analyzers, and some docs. I was vaguely under the impression that the Code of Conduct was automatically synced by some bot from a “upstream” repo to all the other Exercism repos.
I think there’s a difference between the site-wide CoC and the per-repo CoC.
The site-wide CoC was moved to docs/using/legal/code-of-conduct.md at main · exercism/docs · GitHub - and it contains an error there. As @senekor notices, the link in the CoC still points to the website-copy repo. Probably a quick PR would be welcome 
The per-repo CoC is stored here org-wide-files/CODE_OF_CONDUCT.md at main · exercism/org-wide-files · GitHub and indeed whenever it gets updated, PRs with identical changes get opened to every single repo.
But AFAIK, there is no automatic connection between and docs/using/legal/code-of-conduct.md and org-wide-files/CODE_OF_CONDUCT.md that would sync them.
As for the original question
What’s the deal with the website-copy repo?
It used to be used for all user-facing copy in v2. Now in v3, it’s only used for user-generated copy: analyzer comments, mentoring notes, approaches. The relevant directories in there are analyzer-comments and tracks. Everything else is deprecated.