Someone does, but not you. Obviously, there's a server somewhere which runs your code. But since you don't deal with it directly, it's mostly as if there was no server - since it was abstracted away form you so you could focus on what you really want to do.
If you were to go down deeper, a server is just an electrical machine which shuffles eletrons around. So, you could say "there's no point in talking about 'servers', if we're just using transistors when you really think about it".
But it would convey no useful information if someone asked you "what are you using to run your service?" and you replied "well, I just move electrons around", would it?
No, i am not advocating reductionism, server has a analogical meaning as it serves something. Processing has analogical meaning as we do processes something, serverless implies there are no servers involved.
As far as managing goes, most of the server are not managed by you anyway. But yeah i get it, everyone likes it so...
On the management side, I'm curious what you mean by "most of the server are not managed by you anyway". In my experience, unless you're in a very big company, you are either managing or at least minding the server, or someone within earshot range is.
In that scenario, not having to even consider if the error you're getting is because your server is restarting/out-of-memory/needing-update/broken-by-a-coworker like 99% of the time is as close to "serverless" as it gets, in terms of day-to-day work activities and worries.
If you were to go down deeper, a server is just an electrical machine which shuffles eletrons around. So, you could say "there's no point in talking about 'servers', if we're just using transistors when you really think about it".
But it would convey no useful information if someone asked you "what are you using to run your service?" and you replied "well, I just move electrons around", would it?