Lots of potential ways of shaving this yak.
The best “modern” way would be to create a Micropub endpoint and then you can use some of the excellent multi-platform Micropub clients like Quill, Omnibear, Micropublish.net, etc. The benefit of this is that you get way more than just bookmarks.
I don’t know if anyone has set one up to work with Eleventy or Netlify, but there is some prior art for other static site generators.
The low brow solution may be to take the route I took with TiddlyWiki, but that includes some cutting and pasting, so it may be helpful, but isn’t a completely automatic solution. You’ll note there’s a reply at the bottom of the post that modified my code for use with Roam Research which also includes code for browser extensions as well.
If you want to go crazy with some .php, there’s Parse This code for a plugin for WordPress that might be co-opted. It will parse a variety of pages for microformats, JSON-LD, schema, OGP, etc. to return rich data on a huge variety of websites to give you lots of metadata to create a bookmark, but this may be over and above anything you might want. I use it as a built-in product in the Post Kinds Plugin for WordPress to create a wide variety of post types for reply contexts.