In reply to Hugo.

As noted in an earlier content, there were some fixes released in WooCommerce 4.4.1 that should address the issues some stores were seeing with the 4.4.0 update.

Regarding the problems you are experiencing with the WooCommerce Checkout Block, WooCommerce 4.4.0 doesn't have the WooCommerce Cart and Checkout blocks in it. Instead those blocks are found in the feature plugin. Could you point to where you reported the issue you are experiencing with the checkout blocks so I can make sure it hasn't been missed please?