For anyone who finds this in the future, I was able to solve my problem. I ordered a new battery from another source that worked. I noticed that my battery was 11.52V and the one iFixit sent me was 11.58V. I saw a mix of both voltages when searching for this replacement online. I selected my exact model number when I ordered it, but it seems like maybe there are some differences the model number doesn’t account for or that this site is unaware of. I notice that everywhere it says X1 Carbon gen 5/6. Perhaps they are grouped together because they have the same physical form-factor but don’t use the same voltage? It would have been nice if iFixit sold both or at least warned you to check that this matched before ordering the replacement.