It's simple, you have to first save game to the cloud manually. After that, on the new phone you just use same google account as on the old one.
Then install game from play store, restore purchase, and again manually restore game from the cloud.
This works if you stay within same platform, ie...
I think it's in a way more on iOS and Apple to enable easier life for small developers.
Apple has long standing reputation for being extremely closed platform, not only on phones and tablets, but PC as well. It is good in some ways, but bad in others.
Saved file works on all platforms without problems, if file isn't damaged or corrupted in any way (which isn't responsibility of the game itself).
I don't have iOS, but I did exchanged files between my PC and phone (Android). And, only "problem" is, how to access file system on iOS. If you know...
Each platform (Android, iOS, Steam, GoG) is own company, and you have to buy it again, in each corresponding store.
But, save file works on all devices and platforms, if you want to exchange it between devices.
I actually prefer to play it on a PC, just because of how you control movement. But, I know it's personal preference, so I can't tell what you would find more suitable.
Also, you can play only with mouse. And with controller too.