I think they listed it on ebay because they were replacing the battery and didn’t knew what to to with the old and got the idea that they are listing it on ebay to make some money. Imagine if someone bought it and thought that is a new battery
Did you tried replacing the battery? It can be an issue with your laptops logic board or it can be a faulty connector or a battery. Try opening it up and checking on the battery connector’s condition or any corrosion on the motherboard.
I think you’re using a different model of a macbook air because the 2014 model has a different battery connector that you shouldn’t lift up bcs you can broke it