Web components are a low-level primitive - they are clunky to use directly.
Polymer and LitElement - are libraries - you can author WC's with them. And yes they are different (I used both), but you don't really have to migrate from one to another.
Web components are not divided - Lit-element can work within vuejs or polymer or angular for example. VueJS authored WC's can work within lit-element or polymer.
https://custom-elements-everywhere.com/ - see this for more information about interoperability (sometimes it depends on templating syntax).
You asked about Svelte and Stencil - https://svelte.technology/, https://stenciljs.com/ - those compile your code into web components - different approach than polymer that is a suite of quite a few higher-level abstractions that you might not want to pay for (20kb of js).
Don't know what you mean by saying it has no relation; I've been using that site for searching components while developing my PWA based on Polymer. I can install components with yarn or npm just fine, using instructions and examples from there.
You named Web Components, I've been embracing them for a while, but if you tried to switch from Google's Polymer to LitElement it wouldn't go smooth as you could have imagined. Both Polymer and LitElement are based on Shadow Dom and WC features curated by Google, but are not 100% backward compatible. That is to say, Web Components have been divided from within the same tech. No need to mention the rival concepts of "everything HTML" of Polymer 2.0 and fixing it to be "all JS and webpack-ready" in 3.0, and consequential deprecation of Bower.
And here you mention some Svelte and Stencil which I've never heard of before. Why need them? We have webcomponents.org already.