proxy_buffering defaults to on. nginx reads the upstream response into memory buffers and only begins sending to the client once a buffer fills or the response completes. For a normal response this is desirable, because it frees the upstream connection early. For a stream it means nothing reaches the client until several kilobytes have accumulated, which looks like the endpoint hanging.
This affects server-sent events, chunked progress output, and token-by-token responses from a model API proxied through nginx.
Turn it off for the affected location with proxy_buffering off;. The upstream can also disable it per response by sending the X-Accel-Buffering: no header, which nginx honors and strips, and which is preferable because it keeps buffering for the endpoints that benefit. For SSE also set proxy_cache off; and raise proxy_read_timeout, whose 60 second default closes an idle stream. Note that gzip on reintroduces buffering for compressed responses, so a stream can stall again after buffering is disabled if compression applies to its content type.