Why wont my iPad air upgrade to iOS 15 Its stuck on iOS 12.5.5 and my iPad tells me my software is up to date

Because an iPad Air 1st generation cannot support iOS versions beyond 12.5.5, due to hardware (CPU/RAM) incompatibility, as per this chart:

Insofar as your iPad is capable, its system software is up to date. The first generation iPad Air, iPad mini2 and mini3 can only be updated to iOS 12.5.5.

Apple ended major update support for these models of iPad in September 2019 - although they since continue to receive occasional “point” security updates - the most recent being released late last year. These devices cannot be updated to iPadOS 13 (or any later major versions of iPadOS) as the internal hardware does not meet the minimum technical requirements (CPU and RAM) for newer versions of iOS/iPadOS.

Some App developers have dropped support for iOS versions preceding iOS 13.x for technical reasons (often because APIs or software libraries upon which they rely have been updated in the new version of iPadOS, making their App incompatible with earlier versions). 

Whilst many App titles remain compatible with your iPad, if you want or need to access to Apps requiring the most recent versions of iOS, you’ll need to consider replacement of your iPad with a newer or current model that supports iPadOS15.

Sorry, I appreciate that this may not be what you were hoping to learn.

I hope this information provides clarity as to your available options - and the fundamental limitations of your iPad.

All computers have a finite lifetime through which its system software will be updated by its manufacturer - this being true of all operating systems. Your iPad Air1 has been receiving updates for nearly eight years from its initial release.

Apple are perhaps unusual in providing active support typically for five to seven years (sometimes longer), whereas most others will cease support much sooner.

Consider that Android devices typically have a support life from their individual manufacturers of perhaps two to three years before update support is lost; some Android devices never receive a system software update, being effectively obsolete immediately upon release.

While the choice is entirely yours to make, if you have already invested in App purchases, perhaps staying within the Apple family would be in your best interests. App purchases are not transferable between platforms - such as Apple to Android and vice-versa.

You're welcome, Carlos.

Yes, unfortunately your device (firstly released in 2013) is too old to run current iPadOS versions.

Regards

Giulio

How to do update manually?

What does “update manually” mean? There’s no special way to “manually” update a device beyond the last update it supports.