I flew in to Abu Dhabi, stricter Covid-wise than Dubai, without a smartphone in late March. No need to install the app - the staff who did the PCR test on arrival didn't even mention it. You're right, lots of the UAE government information online is confusing or seemingly inflexible, but coming as a tourist you'll be fine.
Since the original question was posed, another possibility has appeared: Google Fi.
One must have a US account and live (mostly) in the US. However, significant overseas use is inexpensive and the service reaches a lot of countries. Android devices work best; iPhones are possible with some features not working quite so well.
EDIT June 8, 2021: several ...
Option 3 with the local SIM cards is not that easy anymore. At least in germany the providers are required by law to check your ID. While you can still buy a card at aldi for example, you need to activate it online or offline. Not even sure it works at all without a german passport.
If #1 is not possible, in my opinion #2 is the way to go.