What does “processing” mean?
The processing status is meant to be used as a step in which the store is preparing or processing the order. Normally meant for shippable items but also in some cases for virtual items.
In this sense having an order in processing status does not have any impact on the enrolment status for your students. In other words: a processing order will still grant access to the student to the course she purchased.
How can I get them marked as “completed”?
You can mark the orders manually but in case you don’t need to do any manual review you can mark the WooCommerce Product as Virtual and Downloadable.
When has this changed?
Previous to Sensei Pro 1.11.0 we were marking all the orders as completed but some users had a valid usage for the processing status.
Since we were changing how WooCommerce orders normally work we stopped doing that starting from Sensei Pro 1.11.0.