Stuller API WooCommerce Integration

I need my WooCommerce store fully wired to Stuller.com through their API so products, prices, and orders all move automatically—no more manual uploads or edits. The scope covers three core flows: Product synchronization, Price updates, and Order processing. I expect real-time sync, so please design callbacks or webhook style listeners rather than periodic jobs; however, background processes will still be needed for resiliency, so you’ll be setting up the first round of cron jobs from scratch.

Here is what a successful hand-off looks like:

• A working API connection authorised through my Stuller credentials and mapped cleanly to existing WooCommerce product types, including variations where applicable.
• Real-time push/pull of inventory, pricing, and order status with graceful fall-back to scheduled tasks if webhooks are delayed.
• A simple, front-end “configurator” flow that lets shoppers select options supported by Stuller (metal, stone, size, etc.) and passes those choices through to the API without breaking WooCommerce checkout.
• Robust error handling: meaningful logs in wp-content, email/Slack alerts for failures, and automatic retries.
• Clear documentation in a markdown file describing endpoints used, custom hooks added, and how to adjust cron timings in case I need to.

Please outline your approach, preferred libraries or plugins (if any), and a realistic timeline; I’m ready to start as soon as you are.