In order to bring this companion app to iOS I tried some things with web apps (installed via the browser, not the App Store), but it did not work out.
It seems I need an Apple Dev account and a Mac to build the app. But instead of buying a Mac for about 1.800 € I found some cloud based services to rent one.
If you want to support me in bringing this and future apps and games to iOS, you can donate via my GoFundMe campaign. The funding goal is 200 €.
Thank you for your time and support.