MySQL installation failing - root password required

I installed mysql-server via apt install mysql-server. It seemed to go fine. However, when I enter sudo mysql to set up a root password, I get:

ERROR 1045 (28000): Access denied for user 'root'@'localhost' (using password: NO)

Which is interesting, because none of the documentation I’ve seen says that I need a password. I tried sudo mysql -u root -p and hit Enter at the password prompt, but I got the same result.

Next, I decided to try sudo mysql_secure_installation. No luck - it asked me for the root password, which I had not yet been able to create. Hitting Enter got me:

Error: Access denied for user 'root'@'localhost' (using password: NO)

I.e., the same message with a different prefix.

I dug a little bit and found the suggestion to stop the service and start it with mysqld_safe. That failed in a different way:

[1] 17293
~: 2022-06-20T00:07:01.652212Z mysqld_safe Logging to '/var/log/mysql/error.log'.
2022-06-20T00:07:01.654424Z mysqld_safe Directory '/var/run/mysqld' for UNIX socket file don't exists.

[1]  + done       sudo mysqld_safe –skip-grant-tables –skip-networking

And indeed, /var/run/mysqld don’t exists. I created it and tried again:

[1] 17776
~: 2022-06-20T00:13:33.123633Z mysqld_safe Logging to '/var/log/mysql/error.log'.
2022-06-20T00:13:33.154910Z mysqld_safe Starting mysqld daemon with databases from /var/lib/mysql
2022-06-20T00:13:35.950220Z mysqld_safe mysqld from pid file /var/lib/mysql/ocean.pid ended

[1]  + done       sudo mysqld_safe –skip-grant-tables –skip-networking

It took roughly a second to start and then end. /var/log/mysql/error.log had no new messages. /var/lib/mysql/ocean.pid was nowhere to be found.

Finally, I tried a suggestion that had me updating the contents of /etc/mysql/my.cnf. All of the commands - mysql, mysql_secure_installation, mysqld_safe - gave the same results, so I reset the my.cnf file to its former state.

To summarize, thus far I simply can’t use MySQL, because it’s asking for a root password that it won’t let me create. Any thoughts out there about what might be going on?