This means that if you have the multiple instances of the same web component on the page, you need to duplicate the whole style tag in each (right?), which seems unwholesome.
What I'm saying is that if you inline your styles in a style tag (either in the shadow DOM or in the head of the document) then the browser doesn't have to make any additional requests at all, because the styling information is present in the initial document already.
If you don't inline your styles, then the browser has to make two separate requests if the cache is empty: one to fetch the document and figure out which additional resources need to be loaded, and then an additional request to actually download those resources. There's no HTTP protocol shenanigans or link preloading that can change the fact that packets are being transmitted from the browser to the server and back again twice. It's basically another formulation of the N + 1 query problem. Once the CSS file has been cached you only have N requests instead of N + 1, but then the cache has to be invalidated every time you update your styles so you're back to square one again. The documentation for Lit explicitly recommends avoiding external stylesheets for web components, because it can lead to a flash of unstyled content while the browser makes an additional request to load the external styles: https://lit.dev/docs/components/styles/#external-stylesheet
If you place the link element inside the head of your document, then it is render blocking, which means the browser has to make two round trips to the server if the CSS file isn't in the cache before it can render (one to download the HTML file, and then another after it discovers your link element, and has to download the corresponding CSS file).
> The best from both worlds is to embed a lightweight basic CSS stylesheet inline and the rest in cache-able external CSS files.
This is the absolute optimal way of doing it. You would have to analyze your styles to see which styles are applied to elements above the fold, then extract them and put them in an inline style tag. The rest of the styles would have to be downloaded via a link tag, but you'd have to place the link tag at the very end of the HTML body tag to prevent the browser from blocking as soon as it encounters the link element or alternatively use JavaScript to add the link element after the page has been rendered. There are tools to automate this for static sites [1], but doing this for dynamically generated HTML is kind of a pain, and I've found that browsers parse CSS so quickly that the overhead of just inlining it all is very low in many cases.