Does the cloud Webflow MCP work with the Designer, or only the CMS?

Both. It's a myth that the cloud version is data-only. The cloud MCP exposes the full Designer toolset (elements, styles, components, variables) as well as the data tools (CMS, pages, assets, publishing). The thing that actually controls canvas access isn't local vs cloud — it's whether the Bridge App is open in the Webflow Designer.