Yandex is king
After both Google and Microsoft enabled creation of custom emails only for paid plans, one of the only email providers standing is Yandex Mail.
First we will go to https://mail.yandex.com/ and create new Yandex account which will be organization-wide admin account.
Login to newly created account on https://mail.yandex.com/ and then go to https://connect.yandex.com/portal/services/webmaster.
Adding a new domain
As an option choose DNS and add TXT record to your domain provider's DNS zone.
Adding user accounts/custom email prefixes
To create a new email account go to https://connect.yandex.com/portal/admin/users/
Then click Все сотрудники and add a new user by clicking "Add" and choosing "Add a person".
You can also create mailing lists by "Creating a department" and adding people to it.
If You want to create a new email for the same domain later, you can do it but only from the admin firstname.lastname@example.org account that you've created at the beggining as it is only admin account in your organization.
If You know about other great Yandex functionalities, leave them in the comments :)
Thanks for reading through!