For others who might be in a similar situation, a brief description of our initial site setup and solution to the upgrade issues:

The site was set up on a shared host which uses cPanel and Softaculous. The install version 12.X was done with Softaculous. The cron jobs were set up following some cPanel instructions. Una 12 is based on PHP 5.6 which I had chosen via cPanel. When I set up the cron jobs initially, they were hard coded to PHP 5.6. I changed them somewhere along the way to PHP 7.2. The Una upgrade docs say that there is a change to PHP 7.4 at 13.0.0-B2. I tried various iterations of the upgrade restoring files and database from backups each time. The main issue was that the modules did not upgrade at each step. This was due to the PHP 7.2 hard coded into the cron jobs.

Ultimately, the solution was to start with 12.X, change the PHP version in cPanel to 7.4 and change the hard coded PHP version in the cron jobs to 7.4. Then start the upgrade process. After each upgrade, wait a bit for the cron job to run and the modules will be automatically updated (mostly) then check that there are no modules to update manually. If there are, then update them manually before upgrading to the next level. As @LeonidS mentions, there was a spot that it got 'stuck'. I think it eventually got there, but it was late and I went to get some sleep. He finished the upgrade for me and I am very, very appreciative of his help with this.