> how would they know if my requests are originating from Claude Code vs. OpenClaw

How wouldn't they know? Claude Code is proprietary they can put whatever telemetry they want in there.

> how are we violating... anything? I'm working within my usage limits...

It's well known that Claude code is heavily discounted compared to market API rates. The best interpretation of this is that it's a kind of marketing for their API. If you are not using Claude code for what it's intended for, then it's violating at least the spirit of that deal.