Can I download an apk of an app I have payed for?

So my dilemma is that I paid for Minecraft PE some years ago, but then I deleted my Google Play Store account, and got a **new one**. * What I'm wondering is if it is okay to download the apk because I'm not paying for it again, and I think it would because technically an apk file is kind of like a rom backup of a cartridge game and those are legal to download if you own a legal version of the game * My issue is that I'm downloading the apk of the newer update then I bought, so is it legal? Since the version of game is different from what I have purchased