How are you installing the chrome-types package? I installed it in my project directory and VS Code picked it up without any special configuration. Here's what I just did just now to verify things were working as expected.
1. cd to a test project directory.
2. npm init -y to create a new package.json with default values
3. npm i --save-dev chrome-types to install chrome-types in this project's directory (and add the dependency to package.json)
4. code . to open VS Code in this directory
5. Create a new js file (e.g. background.js) in this directory, open it for editing, and start typing something like chrome.action.
You should see IntelliSense kick in as you type the word action. If you don't, you might need to give VS Code a couple seconds to initialize TypeScript language features. If that doesn't work, IDK 🤷
Simeon - @dotproto
Chrome Extensions DevRel