Hi,
I ran into the same problem. Apparently mysql in newer versions stores the password of the users differently.
In order for it to work I changed that according to the notes further at the end of this article, to make a) the installation script work and b) make seafile able to open the database later.
ALTER USER ‘root’@‘localhost’ IDENTIFIED WITH caching_sha2_password BY ‘password’;
ALTER USER ‘seafile’@‘127.0.0.1’ IDENTIFIED WITH mysql_native_password BY ‘password’;
As you were able to verify the root during installation, you’d probably only have to change the password storage algorithm of your seafile user.