How transfer account between devices (android to android)?

My MIL recently gave my wife an extra tablet she had for whatever reason, but my wife doesn't really have a need for the tablet or use it often so I was using it sometimes to play mobile games. I gave this game a chance a few days ago and was really enjoying it, but my personal laptop stopped working recently, I haven't had time to troubleshoot it, and now my wife is using the tablet a lot more.

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What I am trying to do:

I downloaded BlueStacks, an android emulator, onto my outdated but still decently-powerful gaming pc, and logged into the google account, downloaded LDoE and tried to play. But my account from the tablet was not loaded and it's making me start a new game. I did some research and it seems that using your google games account should allow for seamless device-switching but I don't know why my account didn't sync.

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Are there any troubleshooting steps I can try to resolve this?

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I've identified a list of pros so people won't have to ask why I am doing this:

I'm not hogging the tablet

No need to charge an emulator during my long-ish play sessions

Tablet seems a little outdated/underpowered, I'm hoping I can play with higher graphics and/or higher fps

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Thanks