484588 is the dimensions of the battery. So 4.8mm thick, 45mm wide, 88mm long. Any lipo that fits in there will do the trick, but obviously similar size is best. You should be able to find something similar on AliExpress; it would help to round the dimensions to a more standard number. For example, search "504090 3.7v" assuming a 5x40x90mm battery would fit in the cavity.
Thank you so much for your help! If you don't mind a follow-up question from a novice: do I not have to worry about matching the mAh and Wh ratings, as long as I match the voltage rating?
mAh/Wh is just the capacity of the battery, and it's often exaggerated or just plain incorrect on these cheap mass produced batteries. So battery life may be slightly different than intended for the product but it won't cause any issues. As long as voltage is similar(all lipo batteries are 3.7-4.2v, some manufacturers label with 3.7, some with 3.8, etc. But all cells of the same battery chemistry are the same voltage range) it'll operate and charge just fine.
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