This is because Sequel Pro is not ready yet for a new kind of user login, as the error states: there is no driver.
mysql + homebrew
Basically you will have to perform some actions manually, however- your database data won’t be deleted like in solution below
Go to my.cnf file and in section
Login to mysql server from terminal: run
mysql -u root -p, then inside shell execute this command (replacing [password] with your actual password):
ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY '[password]';
exit from mysql shell with
brew services restart mysql.
Quick fix (destructive method)
Quick fix for non-homebrew installs:
Apple Logo > System Preferences > MySQL > Initialize Database, then type your new password and select ‘Use legacy password’
After restart you should be able to connect. Do it only on fresh installs, because you may lost your db tables otherwise.
The my.cnf file is located in /etc/my.cnf on Unix/Linux
For those who is still struggling with Sequel Pro problems: Sequel Pro was a great product, but with tons of unresolved issues and last release being dated to 2016 perhaps it’s a good idea to look for some alternatives. There is a fork of SequelPro called SequelAce that seems to be pretty stable and up-to-date, it keeps similar functionality, similar look and feel, yet at the same time it is devoid of old Sequel Pro problems