Having used "the internet" since 1975 (still have the first protocol spec), I would define "internet" as peer connections carrying IP protocol.

We also had uucp net, which was a transport independent store and forward network. We collected all known peer connections in a text file and ran a graph analysis overnight to optimize routes (bang paths) to destinations.

Today, no one seems to know what a "peer" is anymore. From questioning people about what the "internet" is, I get the idea they think it is their web browser. I.e. HTTP(S) is the only protocol they care about (and indirectly though unknowingly DNS and TLS CAs). Even smtp, they have only experienced through some web client (usually gmail).

The term "protocol" is unknown - except in classical schooling groups where they practice social protocols at formal dinners, concerts, and other events. This is relevant, and a starting point.