How do I run mysql_secure_installation on 22.04?

I've just installed MySQL 8.0.36 on Ubuntu 22.04 and now I want to run mysql_secure_installation.

The guide for this precise thing at Digital Ocean indicates that on Ubuntu, running mysql_secure_installation produces a logic loop if you don't configure the MySQL 'root' user's password first. Following its instructions, I did so:

$ sudo mysql[sudo] password for user: Welcome to the MySQL monitor.  Commands end with ; or \g.Your MySQL connection id is 8Server version: 8.0.36-0ubuntu0.22.04.1 (Ubuntu)Copyright (c) 2000, 2024, Oracle and/or its affiliates.Oracle is a registered trademark of Oracle Corporation and/or itsaffiliates. Other names may be trademarks of their respectiveowners.Type 'help;' or '\h' for help. Type '\c' to clear the current input statement.mysql> ALTER USER 'root'@'localhost' IDENTIFIED WITH mysql_native_password BY 'crocodile69210';Query OK, 0 rows affected (0.00 sec)mysql> exit;Bye

After doing this, I am unable to run mysql_secure_installation at all. When I try, I get a password error:

$ sudo mysql_secure_installationSecuring the MySQL server deployment.Enter password for user root: Error: Access denied for user 'root'@'localhost' (using password: YES)

This happens when I enter both the MySQL 'root' user password that I established earlier (crocodile69210) and my OS sudo password. If I enter no password at all, the result is the same except the last line is(using password: NO).

What do I do to be able to run mysql_secure_installation?

Edit: It appears that the ALTER USER statement above does not actually set a password. If I run $ mysql -u root -p and literally copy and paste the password that I set, which is still visible in the terminal history, I cannot login to mysql:

$ mysql -u root -pEnter password: ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: YES)

I'm not sure if or how this illuminates the problem.

Edit 2: Working on the theory that the Digital Ocean guide is wrong, I uninstalled MySQL ($ sudo apt remove mysql-server) and then re-installed it. I did not run the ALTER USER command given in the DO article. I still cannot run mysql_secure_installation and get the same "Access denied" password errors I got during the first attempt.

Edit 3:More information

When I first installed mysql-server from a fully blank slate, I was able to use $ sudo mysql immediately to access the MySQL interactive shell. I find that after 1) uninstalling mysql-server using $ sudo apt remove mysql-serverAND 2) fully purging mysql-server using $ sudo apt purge mysql-server, after I reinstall I still can't use $ sudo mysql. I get the "Access denied" password error. So, something about the first installation is obviously still hanging around. Figuring out what this is will likely help solve the whole problem.