WooCommerce uses Processing for orders that are paid and awaiting fulfillment, and Completed for orders that are fulfilled. For a physical product shipped once, that is exactly right: you ship the order, you mark it as completed, and the customer gets their parcel.
Time-based services do not work that way. A digital subscription, a daily or weekly publication, recurring access to software: no single shipment ends the order. A renewal order pays for a period of service, not a parcel. Left alone, those orders stay in Processing forever, even after you have fully delivered the service for their period.
Complete Renewal Orders completes each order at the moment the period it pays for ends.
⁂

⁂
Does
Backfill existing orders if you ask.
Doesn’t
Autocomplete orders on payment like other plugins do.
⁂
From 49$/y