You neglected to mention the exact model of your MBAir. However, it seems Apple lists the price of a MBAir battery replacement for the 2015 to 2020 models as $160 US. Keep in mind this includes both parts & labor. Even most third party batteries from reputable vendors (OWC and iFixIt) will easily cost $80-$100 US just for the battery itself.
Mac Repair & Service - Apple Support
However, the quality of third party Lithium batteries is extremely poor even when purchased from a reputable vendor such as OWC and iFixIt. The batteries in the 2013-2017 MBAirs are easy to replace. The batteries in the 2018 - 2020 models are replaceable, but they are not as easy since they use about a dozen adhesive strips which unfortunately easily break. Those adhesive strips on the MBAir 2018 - 2020 are made to be removable, but it is very tricky since they must be very carefully pulled, however, if those adhesive strips break, then it suddenly becomes extremely difficult to remove the battery.