I'd love to hear more about your business and what kind of food/service(s) you provide.
At this time, it is not possible to integrate Uber Eats with Shopify. I can definitely understand the importance of having this integration to better serve your clients and business. Rest assured, I'll be passing along your feedback to our development team to look into implementing this feature in the future. I recommend keeping our Shopify Changelog handy to stay up to date for new features that roll out to the platform.