You ran claude mcp add --transport http linkly https://myapp.com/mcp and clicked Allow. Here's everything that happened, one message at a time. Most of it is standard OAuth. The steps marked CIMD are the part that lets any client connect without registering first. Watch the "What each one knows" row: it shows where the secrets, the one-time code, and the tokens are after every step.
Claude on the web works the same way, with one difference: its callback in step 7 is claude.ai/api/mcp/auth_callback on Anthropic's servers instead of a temporary server on your laptop, so Anthropic's servers make the step-8 call. The REST API uses the same login, with resource=https://myapp.com/api/v1 in step 4. Step 5 shows a simplified metadata document; Claude Code's real one may list more fields. Random values like a81f3c… are examples.