The delay depends on a lot of things, from configurable settings for the streamer (both on twitch and on their machine) and for the viewer (low-latency mode, and sometimes, explicitly not! using it), as well as things outside of their control - in Twitch's infra and just general internet latency.
It's not uncommon for streamers to display their chat in a sidebar on the stream, or overlaid on the content itself. From this, I've observed delays as low as (or maybe a bit lower than) a second, and as high as 30s - though I haven't seen anything nearly that high in a long time.
I suspect bigger or more successful streamers are prioritized on Twitch's backend. But I think the threshold for "successful" is actually rather low - someone consistently getting just hundreds of viewers is probably there already, in that top percentile.