In the process of my first update from Drupal 8.7.10 to Drupal 8.8, Update.php would not run to completion because the version of the Pathauto module installed was incompatible. The URL returned the message "the site has encountered a problem..." The lesson here is that all modules should be up to date before updating to release 8.8.
Fortunately, I had enough sense to install a backup of the current live site on my demo account before attempting the upgrade. The initial upgrade (the one that broke) was done on my demo site.
My suggestion is that before updating to a new minor release or even a maintenance release that all contrib modules be updated to prevent the kind of problem that I had with the installation of the minor release. To my knowledge this caveat is not documented anywhere.
I should not admit it, but I have a recently launched site where I neglected to install all of the libraries required by the Webform module. The part of the Webform module that I needed was working, and I had other, higher priority items that needed attention. I don't dare install release 8.8 on that site until I have the Webform module completely installed, and all modules up to date.