Import from subfolder of npm package

Can I skip the src/ directory somehow in the import path?

Yes. Using the package.json "exports" field, which should be supported by Webpack in a near future (see this issue), but has already been supported by Node since Node 12 LTS following the Bare Module Specifier Resolution proposal:

package.json

...
"main": "./src/index.js",
"type": "module",
...
"exports": {
  "./Button": "./src/Button/index.js",
  "./Header": "./src/Header/index.js"
},
...

Now, the following code:

// This project is responsible for building/transpiling after importing
import { Button, ButtonGroup } from 'components-library/Button';

should be translated to:

import { Button, ButtonGroup } from 'components-library/src/Button/index.js';

which should correctly import the requested modules.

Caveat

Now, it would certainly be tempting to try a simpler version like:

...
"exports": {
  "./Button": "./src/Button/",
  "./Header": "./src/Header/"
},
...

so as the usual import statement

import { ... } from 'components-library/Button';

gets translated to

import { ... } from 'components-library/src/Button';

This looks nice, but it will not work in this case, because your submodules don't have each their own package.json file but rely on their index.js file to be found.

/!\ Unlike in CommonJS, there is no automatic searching for index.js or index.mjs or for file extensions.

src/index.js - Is this file actually necessary if only importing from subdirectories?

I don't think so, but you can keep it if you want.

Can I skip any type of build phase in the package?

Using the "exports" field does not require you to transpile your code.

you have to install babel-plugin-module-resolver package

Specify the package relative path in your .babelrc file alias like this

{
  "plugins": [
    ["module-resolver", {
      "alias": {
        "components-library": "./node_module/components-library"
      }
    }]
  ]
}

then you can import subdir of npm package like this

import { Button, ButtonGroup } from 'components-library/Button';

One of the possible solutions there is webpack aliasing system.
You can create another project, call it for example 'app-aliases', so your aliases will be reusable.
This project will has one js file with all of your packages paths:

const path = require('path');

module.exports = {
'@components': path.resolve(__dirname, 'node_modules/components-library/src'),
'@another': path.resolve(__dirname, 'node_modules/any/path/you/want'),
}

And then add it to the webpack configuration in any project which will be responsible for building/transpiling:
webpack.config.js

const appAliases = require('app-aliases');

const config = {
...
  resolve: {
    alias: {
      ...appAlises
    }
  }
}

In the runtime code you will be able to use it like this:

import {Button} from '@components/Button';
import {Something} from '@another'

If you are using typescript you will need to add the same aliases to the paths tsconfig property.
So answers to your questions are:

1. Yes, you can use any path in aliases
2. Yes, it is not necessary to build all of your projects
3. I see that now mui uses imports from directi packages (core for example), see https://material-ui.com/components/radio-buttons/ there is import Radio from '@material-ui/core/Radio';. But I hope they using re-export that I described below.

Also about node.js resolution mechanism.
When you import some library it tries to find node_modules/some-library/package.json and then main property inside it. This property should lead to your main entry point. Usually it is src/index.js (you should set it in package.json if it is no there yet). In this file you can re-export anything you want from internals file structure and will be able to use it without the full path. Please see this repo for some examples.

I'am an angular developer never used react but what I could tell that material-ui are using monorepo where same concept exists in angular where we create one workspace and this workspace hold multiple project/packages as named in react. for more info Workspaces with Yarn

Material-ui using fake paths in tsconfig to make it appears like src folder doesn't exists this from the git you provided: tsconfig.json

This is possible but requires publishing a curated dist folder rather then the root of your project.

The whole thing is rather simple if you understand how module resolution works, and you just need a small script to prepare your distribution.

Lest I repeat all the details here, please see my answer for Importing from subfolders for a javascript package.