Claude reads from .claude/instructions.md whenever you make a new convo as a default thing. I usually have Claude add things like project layout info and summaries, preferred tooling to use, etc. So there's a reasonable expectation of how it should run. If it starts 'forgetting' I tell it to re-read it.
No, Claude Code reads the CLAUDE.md in the root of your project. It's case sensitive so it has to be exactly that, too. Github Copilot reads from .github/copilot-instructions.md and supposedly AGENTS.md. Anigravity reads AGENTS.md and pulls subagents and the like from a .agents directory. This is probably why you have to remind it to re-read it so much, the harness isn't loading it for you.