There was a case once a long time ago, when updating WordPress an error occurred and it turned out that the update did not install and the site remained off.
When it was opened, it was displayed:
“Briefly unavailable for scheduled maintenance”.
In this case, you need to delete the .maintenance file in the wp-admin directory, and also make sure that the WP_INSTALLING parameter is false and not true in the wp-activate.php file.
That’s all, after that you can try to update again.