When a tool says files stay in the browser, the bytes are read with the File API and processed in a worker or WASM module. They are not posted to an upload API. Closing the tab drops the blobs, unless you downloaded them.
That statement is not used for the direct-file fetcher. That tool requests a URL you paste, so the host of that URL sees your browser's request. Social pages may load an official embed, which contacts that platform.
The admin control plane stores campaigns and settings, never visitor media. If the admin API is down, the last published pages and the local tools still work.