Claude Code stores MCP servers in ~/.claude.json (for user-scoped and local-scoped servers) and in a .mcp.json file at your project root (for project-scoped servers shared via git). That is different from Claude Desktop, which uses claude_desktop_config.json.
Claude Code stores MCP servers in two places depending on scope — and neither is the claude_desktop_config.json people often look for. Here is exactly where to look.