Sorry for writing too much, and a bit tangentially, but I think these are valid points, so bear with me:
The utility of any given word is derived from the ability of people to understand what it means. Generally speaking, in this context, it’s also preferable that the meaning be as clear as possible to the layman.
Anytype isn’t the greatest in that regard: anybody who uses the software for the first time needs to learn the jargon of object, type, template, relation, set, etc. It’s not terrible for geek types eager to use beta software, but jargon only adds complexity/confusion that could be avoided by using better terms. (Same goes for “entering the void”…)
As for “Library”, you’re probably correct in pointing out that the Anytype-meaning isn’t intuitive, but it’s not as if computer science lingo will help. In that regard, ontology and vocabulary are equally confusing for the layman.
What’s called a Library is more like a “tool library”, where you can find Type-objects that will serve different purposes/needs. The purpose of the Library, as I understand it, is to say to new users “see all the different things you can do with Anytpe”. So you want to collect recipes? And track movies you’ve watched? See, you can do it all with Anytype and it won’t turn into a giant mess. Each object has its relevant Type, and Types can be arranged in Sets, so your recipe won’t mix with the movie review. And then, of course, the other need for Library is to have a place to manage existing Types.
If that’s the case, other words that could replace Library are inventory and catalogue, but as single words neither clarify that’s where different Types are listed. So maybe “Type library”, “Type inventory”, or “All Types”? I’m not keen about “Set” either, but as long as that’s the word used in Anytype then the Library really is a "Type set" or “Set of Types”. Click on any Type object under “My Library” and you’ll get a set of objects of that Type. (Except that for some reason you can’t filter that set in My Library.)
And then there’s the Anytype Library which has it’s own issues (it should be “add”, not “install”, and you should be able to “remove” it in the Anytype Library without switching to My Library, etc. etc.)
There are other UX issues with the Library making it confusing, but I think a very basic thing would be to have each Type come with a ready-made template. If somebody would like to create an object of that type but start with a “blank” object, give them a button “clear template”. If a Type has multiple templates, apply automatically the one selected as default, and have a button “select template”. Finding where to select the default Type for new Objects is confusing as it is.
(And I’m not even going to go into how Layout is a template, but not a Template…)