Am I able to delete the app to make an in-app purchase and re-download to continue where I was?

I am playing Choices on my iPhone 12 ios 15.4.1. While my diamonds are never used, there isn’t an option to have unlimited keys within this version and I wanted to purchase some. I tried the free in-app purchases switch but it did not work and I also tried entering my stuff and it did not work either (this was before I read and saw in-app purchases don’t work in this version). I was wondering if I were to delete this version and get the App Store version, would I be able to buy what I want and redownload this version? It is connected to my email account so does that mean the progress saves?

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