Using 13.0-RELEASE FreeBSD 13.0-RELEASE #0 releng/13.0 I had the same issue with mysql57 when running service mysql-server start there would be a message WARNING: failed precmd routine for mysql.
Following the same guides to clean the /var/db/mysql folder did not help. I found no other guides that provided any useful information, besides doing a clean install of FreeBSd. So, I resulted to tracking down the actual error by adding set -x to /usr/local/etc/rc.d/mysql-server and added --verbose to track down that my problem was the naming of the directories in the /var/db folder. InnoDB is looking for mysql-secure and mysql-tmpdir to be named mysql_secure and mysql_tmpdir.
Looking at the output of /usr/local/libexec/mysqld --verbose --help I noticed that there are variables for tmpdir and secure-file-priv that are apparently set in /sur/local/etc/mysql/my.cnf. Though, I am uncertain why MySQL does not create those directories in the /tmp folder during installation.
Additionally, I found that MySQL also failed during installation due to the timezone in my.cnf being set to "America/Los_Angeles". This seems like an issue just with installation as, mysql-server was working with this setting before I uninstalled it