Comment 2 for bug 1776846

On package setup from your log:
mysql_upgrade: Got error: 1045: Access denied for user 'root'@'localhost' (using password: NO) while connecting to the MySQL server

This is usually going through a local socket and needs no Password.
But in your case that socket was not reachable.

I see int he logs that mysql was installed/removed plenty of times.
Could on one of those a config change have been made that breaks this.

If this is all fresh you should consider purging all of mysql to get rid of potentially broken configs. And then reinstall the packages cleanly.
That might resolve your issue.

If OTOH you have special background knowledge why on your system that local socket fails please just fix that and an install/upgrade will work.