Its run on your local device - its just a local devserver that allows Sentry's SDKs to pipe data to it. The overlay (the Spotlight UI) then connects to the sidecar via a Server-Sent Events stream (basically a pubsub HTTP stream which operates unidirectional - think websockets but simpler). This is needed due to the distributed nature of services, but our goal is to push this abstraction into dev servers, e.g. Vite.
Added a ticket to track improving the docs here: https://github.com/getsentry/spotlight/issues/242