If using WooCommerce bookings, can listing owners edit their time availability for bookings or does the site administrator need to handle all booking management?
Yes. When using the WooCommerce Bookings and WooCommerce Product Vendors plugins the listing owner can manage the availability of the booking times, from within the WordPress / WooCommerce vendor management backend.
Disclaimer: The vendor plugins mentioned in this article display the WordPress backend to the vendor when managing bookings. This is a limitation of the plugins.