It can do all those things from the claude code web version.
"i enabled github connector can you see it?"
Answer: "I don't see a GitHub connector in the available integrations. The search only returned a Microsoft Learn connector (not connected). It's possible the connector hasn't fully activated yet, or it may not be available in your current setup. Could you double-check in Settings → Integrations that it shows as connected?"
Multiple such checks and re-setups do nothing.
It's not an actual MCP. It's just built into the UI.
Anthropic has a lot of stuff that's way more difficult to use because of bad UI, spread over lots of different places.