My macbook air 2014 is stuck in Mac OS 10.9.5 and ni available updates, what to do?

The App Store Updates page only informs you of updates available for the OS you are running.

Installing a newer OS is called an upgrade.

A MacBook Air from 2014 can upgrade to all available OS's including the most recent macOS Big Sur.

As your mac can upgrade to the newer OS's like macOS Mojave 10.14, macOS Catalina 10.15 and

macOs Big Sur 11.4 I would recommend you upgrade to macOS High Sierra 10.13 first.

As you are still on Mac OS X Mavericks 10.9.5 you will find upgrading to the newer OS's a very big change

from what you are used to, so please make every effort to research how this will impact the way you use

your mac and the apps you use. Please read all information included in links below thoroughly and only

upgrade when you are sure you know what you are doing.

The newer OS's like Mojave, Catalina and Big Sur only run efficiently on a mac that has at least 8GBs of RAM memory.

For macOS High Sierra, Mojave or Catalina.

Open Safari and click on this link, 

How to get old versions of macOS – Apple Support

Go to the Download OS section and click on the OS you want to install.

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS ******.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.

If you want to or are able to install Big Sur, open Safari and click on the link below.

How to upgrade to macOS Big Sur - Apple Support

If you are considering upgrading to Catalina or Big Sur be warned they do not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/ then contact the developers of the software to see

if they are offering 64bit updates.

If this is a 4GB RAM MacBook Air, I strongly advise against upgrading it to macOS 11.4 (Big Sur) as it will be an unpleasant usability experience. Speaking from my own experience with this model and RAM configuration.