How and where to store the progress of each player in a game like Hamster Kombat in Telegram?

I want to make a game in Telegram like Hamster Kombat, I’m doing it in node.js (typescript), I’m wondering how the developers of Hamster, for example, stored the players’ progress, a database comes to mind, but I want to understand exactly how to store it.
I asked GPT, GPT said that it is possible to store progress in a smart contract, I have not dealt with smart contracts and therefore I am not sure that this is possible. Who can tell me I will be grateful

I tried to make a smart contract and some kind of nonsense, nothing worked and I began to believe less that this was being done in a smart contract. help)