Claude Code definitely remembers things about you. For just one of the more obvious examples: I was recently asking it to make some suggestions on software alternatives, and part of the answer included (paraphrased) "While a hosted service may be attractive due to your small ops team size, your experience with hosting Linux container-based services puts this squarely in the realm of an option for you." My prompt mentioned nothing about this.

This isn't something that is public knowledge, in the sense that you mean it.

Just earlier today it asked me if I wanted to create a jira ticket for something I asked it about doing. My prompt mentioned nothing about jira.

If you use Claude Code, you might want to take a look at the "auto memories" files that it creates. See "/memory" for some more information.