Is the iPhone 8 too old to use for Uber eats?

No, your iPhone 8 should be fine. The compatability listed is it requires iOS 14.8 or newer. An iPhone 8 is capable of running iOS15.6.

https://apps.apple.com/us/app/uber-driver-drive-deliver/id1131342792

You will best want to discuss this with Uber, as they may have recommendations for their (presumably) dispatching app that (might) differ from their user-intended app, and might conceivably exceed what an iPhone 8 offers, whether that’s due to available free storage or performance or some other features of a particular iPhone.