Ah, I just discovered the problem. It was PayPal-related.
In the PayPal setup of WooCommerce, I entered a secondary email on my PayPal account. This generated the following order error:
Validation error: PayPal IPN response from a different email address ([email protected]). Order status changed from pending to on-hold.
Because the orders had been changed to on-hold they didn’t affect the inventory properly.
When I changed the PayPal settings to the primary email address associated with my PayPal account, the issue was resolved.