Screen mirroring

I perhaps misunderstood your question. A Mac or PC can use the iPad as a second display - but iPad cannot extend its display to a Mac or PC.

In more detail...

iPad Pro is not currently capable of offering an “extended desktop” experience - such as that to which you may be accustomed on other computing platforms. The new Sidecar feature provides limited scope to use iPad as Second screen from Mac - but not the other way around.

Your iPad can drive an external display using AirPlay - or via HDMI (and appropriate adapter where needed) - but neither can re-scale the iPad output to match the native resolution of an attached monitor.

There are some iPad Apps in the App Store that provide some external connectivity options for PC and Mac (such as Duet and Duet Pro). These can be expensive - and have mixed reviews.

Here is a third-party comparison of some of the options - including a detailed look at SideCar.

https://thesweetsetup.com/apps/best-app-for-using-an-ipad-as-an-external-display/

I hope this proves to helpful in guiding you to some of the available solutions.

While you could use the iPad as a second display under Big Sur, it would seem that your 2014 MacBook Air does not meet the requirements. See this, Use your iPad as a second display for your Mac with Sidecar - Apple Support

iOS/iPadOS devices can only screen mirror to a connected TV or external monitor - not to another iPad, iPhone or Mac.

A Mac can extend its desktop display using Sidecar - but iPad cannot extend it own display to Mac.