I solved the problem!
In this case (to set Yandex Mail as an email account on other email clients) you must first setup a new password for Yandex Mail via Yandex's password app.
After you create a new password, you set it now as a new Yandex mail password. After that setting Yandex Mail as an email account in Vivaldi browser works like a charm.
Yandex changed this rule due to security concerns, since vast majority of users use simple passwords.