FYI, the 2014 MBAir is now considered "Vintage" by Apple. If you plan on needing a working battery for it for some more years, then it would be a good idea to replace it while Apple will still perform the repair. A couple years ago, Apple said they would replace batteries for up to 10 years, but provided very little details. The information I have seen mentions in a footnote "as long as parts are available".
Obtaining service for your Apple product after an expired warranty - Apple Support
Apple will only replace the battery once the battery condition shows anything except "Normal" or "Good". Option-click the battery icon on the menubar to get the battery condition (on macOS 10.15+, the battery condition will only show up if it is anything other than "Normal" -- seems showing "Normal" is too much to ask for now). You can also see the battery condition in the System Profiler under "Power" or in the Battery System Preferences in Battery Health.
I believe only AASPs who perform repairs within their own shop will be able to repair a "Vintage" laptop since I have seen mentioned that mail-in repairs are not allowed for Vintage products, so if you are refused a repair at Apple or an AASP this may be the reason, try checking with another AASP.
While OWC sells a third party battery I personally prefer the Apple OEM battery since the quality of third party Lithium-ion batteries is usually very poor. If you cannot get an Apple battery repair, then a battery from OWC is your next best option. Fortunately the battery in the MBAir 2013-2017 is very easy to access and replace unlike other Apple laptop models.