"Serverless" is "I don't have to provision a server, or worry about where it is, or maintain it, or what OS it's running, or any of the other fiddly details."

You define a function, you hand that function to a company, and they make sure it runs when certain conditions are met. You then don't have to worry about the server.

I think the problem is that these terms had meanings before the last five or so years. There are setups that are actually accurately describable as "serverless" - for example, SQLite is called a "serverless database" because it's an embeddable library that just operates off a file as opposed to client-server DBs like Postgres or MySQL.

Yeah. See https://www.sqlite.org/serverless.html

Of course there's still a server. What it means is that you don't have to worry about it.

Instead, you worry about the provider, and when their worries become your worries you hope you're significant enough to warrant worrying about...

It's a misnomer, but the underlying idea has lots of valid uses.