How do I install on Ubuntu 20.04 (LAMP)?
This might be an issue with the new ways MySQL 8 does authentication. 

Read more about that in this answer: What is mysql_native_password?

From the docs: MySQL Secure Deployment Guide  /  Enabling Authentication 

You need to adjust the authentication method for the MySQl user you're using with Drupal (seems to be root from your screenshot). You can't do that through Drupal, you have to login MySQL through terminal or go through some other way of configuring your installed database server.

If switching to the new way of authentication isn't an option then you can change the user to use the old way of authenticating with  mysql_native_password:

alter user 'root'@'localhost' identified with mysql_native_password by 'whateveryourpasswordis';
flush privileges;


After that Drupal should be able to connect with the chosen database.

This is probably unrelated to your problem, but I've had problems in the past with some special characters in the password (not the database name), I couldn't use &amp; nor # IIRC.