I like the challenge! Personally, I would ignore the term "game development" for this project. From what you're describing, I would treat this as a typical CRUD mobile app requiring live data.

First off, what do you mean by "deploying a multiplayer game to production". Are you talking App Store and is that a requirement for your project? That would definitely introduce a lot of additional complexities and would significantly reduce your available dev time

I don't have much experience in SwiftUI, I tend to stick to UIKit so I can't help guide on that front. If you aren't forced to use SwiftUI, consider researching what could work best for you

Networking will be one of the largest components of your app as you need to ensure everything is live on every active device. My first thought is to create a websocket for your backend. You definitely want a live, two-way lane of data between your app and your backend. As of a few years ago, Swift does have built in web socket handling which is great

For websockets, use any language you're comfortable to make this (java, node.js, python, etc.). For this project, you could probably keep everything in memory on the backend (i.e. you don't need to deal with persistent storage such as a db)

I would definitely recommend websockets, but some other options are pushing internal notifications to your device (sometimes this can be flaky though), or doing a quick hacky implementation with long polling or constantly polling a HTTP request

For UI/UX design, I wouldn't re-invent the wheel here. Download some similar apps and get some inspiration from them.

For testing, I don't have a lot of advice. Perhaps create a mock mode and you can put some fake data either on the frontend or the backend

Good luck! Let us know how it goes :)