I just checked what The Galaxy S3 has for an operating system, and what
MDE needs. The GS3 stopped getting updates at "Jellybean." The latest MDE app requires "Lollipop" to run correctly. The Android versions are all sweets in alphabetical order, starting from Cupcake (C) and is currently on Nougat (N). The "O" version is currently being tested.
On the Apple side, MDE require iOS 9.0 or later.
Disney did this because some of the older code was giving the app fits. It had a choice of either continuing to support the older versions, or to steamline the code and say "sorry" to the older phones. The cost/benefit ratio was probably just no longer worth it. Fewer and fewer people are carrying the older phones, so there's not much financial sense to keep spending money and time on development where the returns are diminishing.
Now as for another phone, you don't need a Galaxy S8 or an iPhone 7s to run MDE. for Apple, A well updated iPhone 4s or better should have the minimum requirements to run MDE. An iPhone 6s or greater will be able to run MDE right out of the box, though updating them is always a good idea. On the Samsung Galaxy S side, a well updated Galaxy S4 or S5 will be able to run the app. Any Galaxy S6 or better can run it without updates, though, again, updating them is always a good idea.
So you don't need the latest phone to run MDE. Unfortunately, your GS3 just missed the cutoff. I wouldn't risk just getting a GS4 or an iPhone 4s to meet the minimum requirements. If the Disney app developers raise the bar, then your phone, again, will no longer be able to use it.