Database update not prompting/updating 3.5.8 to 3.6.2

We held off for a bit, but finally decided to do the 3.5.8 to 3.6.2 update.

I had done this on a test site copy of our main site and another smaller site, and both prompted to update the database.

On the main site, it is not prompting me to update the database, and the WC Status page shows it is still at 3.5.8. Clicking on Update Database in the WC Tools doesn’t do anything, and searching Scheduled Actions for woocommerce_run_update does not show anything in any status, as though it never fired.

I looked at the steps that would be run in class-wc-install.php and wc-update-functions.php, and suppose I could run them manually, but I’d really like to know why this is stuck here and how to get past it “normally”.