Did you try running the hardware test? https://support.apple.com/en-us/HT201257 https://support.apple.com/en-us/HT201257 I had a old Air which ran very slowly

Did you try running the hardware test? https://support.apple.com/en-us/HT201257 https://support.apple.com/en-us/HT201257 I had a old Air which ran very slowly and fans spinning like crazy due to a issue with the cable from the keyboard/touchpad. Apparently if the SMC does not get proper signals it will go into a "failsafe" where things work but slowly. Probably not the same issue, but just a little anecdote on a similar symptoms caused by different issues so that nobody gets tunnel vision on the battery, which might very well be the cause in this case.