Typescript module resolution problem when importing from library's subpath without extension

[croraf]

Describe the bug

The application has a default Vite - ts+react template configuration. I try to reference modules from my custom library which has in package.json

  "exports": {
    ".": {
      "import": "./index.ts"
    },
    "./lib/*": {
      "import": "./lib/*"
    }
  }

In the application I try to import the modules:

import Test from '@inxelo/components/lib/AutocompleteLargeDataset2.tsx'
import Test2 from '@inxelo/components/lib/AutocompleteLargeDataset2' // <--- this errors out

The import without extension errors out.

Cannot find module '@inxelo/components/lib/AutocompleteLargeDataset2' or its corresponding type declarations.ts(2307)

If in tsconfig I change moduleResolution: "node" it doesn't error out.

Runtime works fine (in the example it does not work cause it needs additional setup in the code, but in my production it works fine in runtime).

Reproduction

https://github.com/croraf/typescript-import-issue

Steps to reproduce

No response

System Info

System:
    OS: Linux 6.5 Ubuntu 22.04.5 LTS 22.04.5 LTS (Jammy Jellyfish)
    CPU: (16) x64 Intel(R) Core(TM) i9-9880H CPU @ 2.30GHz
    Memory: 26.16 GB / 31.21 GB
    Container: Yes
    Shell: 5.1.16 - /bin/bash
  Binaries:
    Node: 18.20.4 - ~/.nvm/versions/node/v18.20.4/bin/node
    Yarn: 1.22.22 - ~/.nvm/versions/node/v18.20.4/bin/yarn
    npm: 10.7.0 - ~/.nvm/versions/node/v18.20.4/bin/npm
  Browsers:
    Chrome: 129.0.6668.70
    Chromium: 129.0.6668.89
  npmPackages:
    @vitejs/plugin-react: ^4.3.2 => 4.3.2 
    vite: ^5.4.8 => 5.4.8

Used Package Manager

yarn

Logs

No response

Validations

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• The provided reproduction is a minimal reproducible example of the bug.