I suppose the question is, what is a home server these days? I class them as a silent, very efficient machine that handles background tasks for a home, including plex, firewall maybe, nas, automation and a sand pit for learning. If you require more than this, then it is a proper server thats needed, but thats a different story and a totally different price point.
I think that is a good question, and the answer will vary wildly depending on who answers.
From a manufacturer standpoint, there is no such thing as a 'home server' or has only sparsely been produced (unlike a 'home computer' which is its own category). Manufacturers simply make servers, typically rack mount, to go into racks in data centers. The whole idea of replicating this set up in the home is only possible because of the deep discounts these servers undergo after they retire from the data center (many times far cheaper than a desktop of similar specs). And hence this was the original driver behind homelabbing because the possibilities just opened up when the hardware became available.
Fast forward a couple of decades and now desktops also have many similar capabilities as full blown servers in terms of workload, while lacking in some common 'server' features such as out of band management, 10Gb, SAS, etc. So while they can do the job, to me desktops are desktops, and
not servers even if they are performing the same role. My old Dell lga775 desktop repurposed as a NAS isn't a NAS by design, but by usage--the hardware is still classed as a desktop computer by the manufacturer. It is this flexibility in the PC architecture to fit many roles that has allowed it to flourish though, and that extends to desktops, servers, and everything in between.
So to me the definition if something is a server or not is not by the role or function it plays, but by the original hardware definition when made. So many routers that are really supermicro 1U servers are really servers to me and not routers, desktops are desktops, and the only real servers is a real hardware server. ymmv.