The Airport Time Capsule shows on the MacBook Air Network but in the Airport utility The options for configuring do not show up "under other wifi devices". I cannot backup my MacBook Air 13" 2014

We still cannot tell from your information whether you have reset the Time Capsule back to its default settings and have set it up again.

if you have not done this, please consider doing so.

Things are going to really get mixed up with Time Machine when try to revert back to a previous operating system. Please be advised that you will very likely need to erase the the Time Capsule hard drive and start all over again with new backups.

What OS are you running on the MacBook Air (MBA)?

Did this setup work in the past and you did something like upgrade OS so it no longer works?

Best way is to reset the Time Capsule to Factory and reconfigure it.. with Catalina this is near to necessity.

La Pastenague also asked.......Did this setup work in the past and you did something like upgrade OS so it no longer works?

In other words, were things working OK before and you started having problems after you upgraded to Mojave or made some recent change on your Mac?

He also advised that......Best way is to reset the Time Capsule to Factory and reconfigure it.. with Catalina this is near to necessity.

In other words, when you are having problems, it is always a good thing to reset the Time Capsule back to its default settings and then set it up again. The reason for this is that Apple has made a number of undocumented changes to Time Machine in Mojave, which have resulted in a number of issues for users.

Did you do this?

So, if you could clarify on things further, it will help us know how to best proceed.

Reset the Time Capsule to factory and reconfigure it from the laptop.

No files are lost when you reset. Only the current configuration.

I strongly recommend you use very short names, 8 characters, pure alphanumerics and no spaces.

Passwords 8-20 characters but pure alphanumerics.

Let's give La Pastenague the credit for suggesting that you reset the Time Capsule and set it up again, since he suggested this to you in his very first response.

Best way is to reset the Time Capsule to Factory and reconfigure it.