one option would be to use some kind of micro service that would capture Xero webhook anytime invoice is paid (https://developer.xero.com/documentation/webhooks/overview). Next this micro service would adjust inventory in Shopify. To create it you could use app like: https://apps.shopify.com/datajet.
This would require bit of custom logic to be implemented. Send me a dm if you need to know more.
Hi! Check out Shypyard (https://shypyard.io). It's a Shopify integration platform that can help you sync Shopify inventory levels with Xero.
If you're interested, I'd love to set up some time to chat about it. Simply email us at email@example.com Have a great day!