How to use?

• Copy content of vsix-bookmarklet, create a bookmark in your browser.
• Navigate to the web page of the VS Code extension you want to install.
• Click the bookmark you just created, then click the download button.
  
• After download finished, rename the file extension to *.vsix.
• In VS Code, select Install from VSIX... in the extension context menu.
  

How does it work?

microsoft/vscode-python#20184
https://stackoverflow.com/a/38866913/1032492
https://stackoverflow.com/questions/79359919

A VS Code extension's offline install package (VSIX) is available at:

https://marketplace.visualstudio.com/_apis/public/gallery/publishers/${publisher}/vsextensions/${extension}/${version}/vspackage?targetPlatform=${platform}
OLD TYPE: https://${publisher}.gallery.vsassets.io/_apis/public/gallery/publisher/${publisher}/extension/${extension name}/${version}/assetbyname/Microsoft.VisualStudio.Services.VSIXPackage

Take the syntax highlight extension for Vue.js as an example:

https://marketplace.visualstudio.com/items?itemName=liuji-jim.vue

• The itemName query is a composition of publisher and extension name, separated with a dot.
• The publisher is liuji-jim.
• The extension is vue.
• The latest version number is in More Info section on the right side.
• The platform is hidden. You can check full list of platforms in bottom section. If *.vsix is download without @ symbol in name, than it does not have different platforms.

So the package can be downloaded via this URL:

https://marketplace.visualstudio.com/_apis/public/gallery/publishers/liuji-jim//vsextensions/vue/0.1.3/vspackage?targetPlatform=win32-x64
OLD type: https://liuji-jim.gallery.vsassets.io/_apis/public/gallery/publisher/liuji-jim/extension/vue/0.1.3/assetbyname/Microsoft.VisualStudio.Services.VSIXPackage

Some words about targetPlatform

This example is for Windows x64-bit platform. If page not found, than you should delete platform query: ?targetPlatform=win32-x64.
The full list of platforms that extensions could have are: win32-x64, win32-arm64, linux-x64, linux-arm64, linux-armhf, alpine-x64, alpine-arm64, darwin-x64, darwin-arm64, web (c) @nervous-inhuman

Copyrights and thanks:

• Original Gist: @wanglf
• Another JS: @ShortArrow (check out full rust project)
• Another JS: @mjmirza
• Another JS: @AdamUnderstand