PhpStorm Laravel trying to connect to MySQL database throws java.net.ConnectException: Connection refused: connect

Question

I am trying to set up a laravel project in phpstorm but fail at connecting to a mysql database. These are the steps I've taken so far:

1. download and install composer, vagrant and virtualbox
2. create laravel/laravel project with composer (create composer project in phpstorm)
3. integrate laravel/homestead with composer: composer require laravel/homestead --dev
4. build homestead in root dir: vendor\\bin\\homestead make (windows)
5. personalize my local domain by setting it in Homestead.yaml -> sites -> map: mydomain.com
6. integrated the domain in c:/windows/system32/drivers/etc/hosts: 192.168.10.10 mydomain.com
7. create empty ssh key for vagrant to run: fsutil file createnew C:/Users/<username>/.ssh/id_rsa 0
8. start VM with vagrant: vagrant up

So far so good, everything seems to work. And here comes the problem:

9. create mysql database with phpstorm's integrated database tool, using .env as reference (DB_CONNECTION=mysql, DB_HOST=127.0.0.1, DB_PORT=3306, DB_DATABASE=laravel, DB_USERNAME=root, DB_PASSWORD=devpw)

After installing drivers when trying to test connect:

[08S01] Communications link failure The last packet sent successfully to the server was 0 milliseconds ago. The driver has not received any packets from the server. Communications link failure The last packet sent successfully to the server was 0 milliseconds ago. The driver has not received any packets from the server. 

Or in the log:

java.net.ConnectException: Connection refused: connect. 

I've been trying to find a fix for some time now without success. This Thread seems to provide solutions, many of which I am not sure how to implement, since they are not directed at phpstorm. I feel a bit overwhelmed by the whole backend thing and how to set it up right in laravel.

Am I supposed to install mysql on windows before integrating it into phpstorm?