Your MBA is a "Mac model with Touch ID" so you're good there.
You say the Touch ID rarely works, so that may be part of the problem here. If the feature is broken then it stands to reason that Apple Pay also won't work.
Have you taken steps to get Touch ID to work, like delete and then re-scan your fingerprints?
Manage Touch ID fingerprints - Apple Support
Another troubleshooting step is to boot the Mac in safe mode.
How to use safe mode on your Mac - Apple Support
Does Apple Pay work while in Safe mode?
If so, this may be an indication that there is some third-party app or utility that is interfering with the proper operation of the OS.
You can exit safe mode by restarting your Mac normally, then reevaluate the problem.
Have you installed any anti-virus, clean up, security, optimizing or VPN software on your Mac?
If so, there's a very high chance that it may be interfering with the OS. Apps of these types often cause more problems than they prevent. You can safely uninstall those apps. They aren't needed. The Mac has built-in features to address these issues.
Meanwhile, as a work around, if you have an iPhone or iPad you can use that to authenticate your Apple Pay purchases on your Mac.
❝On Mac models without built-in Touch ID, you can complete your purchase using Apple Pay on your compatible iPhone or Apple Watch: On your iPhone, go to Settings > Wallet & Apple Pay and turn on Allow Payments on Mac.❞
