I understand both what you say and what "serverless" commonly means, I'm just saying it's essentially arbitrary. A symbol with no etymology that holds water.
Understandably, if you don't come from the software world you might think a server is a person who does work at your request, like serve you food at a restaurant. Is that where the problem lies? There are definitely still people, servers, serving the care to the systems that run the software. But that is clearly not the context in which it is used. It is very much used as a software term, and as a software term alone.
This might be why people are having trouble with it. "Cloud" and "serverless" both refer to hardware, not software.
"Cloud" was moving the hardware from something you managed, either in office or a datacenter, to using machines someone else managed, but it was still server-oriented (such as software in VMs or bare-metal that you managed).
"Serverless" drops even that, using ephemeral code that doesn't care what server it's running on, so the people managing the hardware can move your software as-needed.
Not really. "Cloud" refers to a software abstraction that tries to hide the existence of actual hardware namely to remove dependence on the availability of any specific hardware component (like, as in, being able to transparently move to another physical machine without the user ever knowing). It is clearly a software term. I can't go down to my local Walmart and buy a "Cloud". Amazon won't ship a "Cloud" to my place. There is nothing "hard" implied by the word as used in this context. I'll grant you that it more or less maintains some kind of "virtual" hardware concept. Perhaps that is what you mean?
There is no hardware association with "serverless". It refers to a pattern for developing a certain breed of applications that resemble servers, but without the server. "Server" is definitively a software term as used here. A server is an application that listens for requests from a client, typically on a network port if we are to dive into implementation territory, but could be something else like a unix domain socket. Much like CGI of yore, these "serverless" applications shed the server, relying on the runtime environment to fill in the missing pieces.
You are describing a thing that is not a foo, or does not do foo, not a thing that posesses no foo.
So, I say, this is just something you're saying and not a definition I ever heard or would have implied from context from others usage. And it's not a new term by now, so there has been several years for me to have gained this impression or understanding if anyone else were using it that way.