>I don't really grok how they fit into the greater internet or how their hosting works or why you have to pay a separate provider
In much the same way that you need a specialized email client to use IMAP/SMTP, you need a specialized client that speaks NNTP to access usenet.
The providers are heterogeneous but usually are basically beefy servers connected to fat pipes to handle the massive volume of traffic, which is why you typically need to pay for access.
st is actually one of the worst terminals available. For all their purported minimalism, it has abysmally bad performance. See https://danluu.com/term-latency/