How can I get VSCode auto-imports working in a TypeScript monorepo?

I have a very simple TypeScript monorepo with the following structure:

project/
└── packages/
    |── client/
    ├── server/
    |   └── src/
    |       └── main.ts
    └── common/
        └── src/
            └── main.ts

The server has a package.json file with:

  "dependencies": {
    "common": "file:../common"
  },

And the code looks like this:

// in file: common/src/main.ts
export class Foo() {}

// in file: server/src/main.ts
const foo = new Foo();

When I open VSCode, put the cursor over Foo, and do Ctrl+Space, it doesn't find any imports. But if I manually add import { Foo } from "common" to the top of the file, it compiles and works just fine. Why doesn't auto-import work? How can I make it work?

For reference, the above reprex is available to download in a repo located here: https://github.com/Zamiell/test-monorepo