Can't download any Applications on my MacBook Air

User wrote "osx" denotes OS X 10.12 Sierra released in 2016

The moniker was re-branded " macOS " starting in High Sierra macOS 10.13 released 2017.

To download Xcode from Apple would require a Qualifying Computer to run macOS 13 Ventura .

The Age of this computer will Govern what newer version of macOS it will Qualify to install. 

Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.

Does this computer appear as Listed and qualifying for an upGrade to a newer version of macOS ? 

Safari will open a redirect and open the Apple Store where the download can commence.

If Yes, suggest having at least 50 GB of Empty Space on the drive.

It will allow the Full Version ( about 12.xx GB ) to download, expand and then commence to install.

If there is Third Party Security Software installed - remove it.

It will interfere with both the download and installation process.

The below links will help identify which version of macOS  this computer may Qualify to run.

macOS Sonoma is compatible with these computers

Computer Qualifying for macOS 13 Ventura 

Make Time Machine Backup  before doing any upDates / upGrades 

I am very sorry, I gave you the wrong advice.

The current version of Xcode is used to develop software for current Macs, iPads, or iPhones. If you are not developing software for the latest Apple devices, Xcode is of no value to you, and whether you can download the current version is of no consequence.

To do that sort of development, you need to be running very nearly the absolute latest version of MacOS on a fairly recent Mac, almost any model.

I mistakenly assumed that you had all the other prerequisites, and read your MacOS High Sierra 10.13 thinking that you had Ventura 13 already installed.

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if your Mac is actually running 10 13 High Sierra, what else (other than Xcode) would you like it to be doing for you that it does not already do?

what model year is your Mac? and is it in fact the MacBook Air?

 menu > about this Mac ...

...to get the answers

if you are actually running Ventura, as your equipment line says, the latest version of Ventura is 13.6. You should update to at least that version, to avoid discovering bugs that may have been already found and fixed.

The current version of Xcode appears to be version 15.2, which says it requires macOS 13.5 or later.

More so, conflicting or incomplete accurate information from OP rather oversights by yourself IMHO