Back then, an internet (lower case “i”) was a small internal network of computers that communicated with each other.

That’s what I was told too, but I never once encountered anybody who used the small-i “internet” term. I heard “network”, or “intranet” or often topology-related things like “the token-ring network”. Maybe that’s just me, but I suspect that small-i “internet” was never really a term that was widely used, if at all.