> I wasn’t sure how to find out what an “LI????77” was […]. I would be interested to learn non-LLM ways to figure this out though. There must be a way.

Reading https://en.wikipedia.org/wiki/Button_cell#Type_designation would have indicated a solution: The third character must be an R (for rechargeable), the “77” would be the height in tenths of millimeters (which makes for a good plausibility check), and then you can measure the cell’s diameter to obtain the remaining digits in the middle.