How do I run Apple Hardware Test on a 2012 MacBook Air with 10.15.7?

See the following Help Topic for help in running Apple Diagnostics/Apple Hardware Test on your MacBook.

If you still have trouble, scroll down to the bottom of the linked page and see the info under Learn more

Use Apple Diagnostics to test your Mac - Apple Support

The online Apple Diagnostics leverages the same framework as Internet Recovery Mode uses. It is perfectly normal although confusing. Select & connect to your WiFi network and assuming a good network connection, hopefully you will see the Apple Diagnostics. Unfortunately Apple has broken this with some Macs, so if you instead encounter an error message which includes something like: "Cannot Load EFI/Drivers/TestSupport.efi", then it means you won't be able to run the diagnostics due to a compatibility issue Apple introduced & decided never to fix.

In that case, tell us what problem you are having with your laptop as we may be able to offer solutions on how to identify the source of the problem. Posting an EtreCheck report would be needed as it would give us details about your Mac (assuming you can still boot the laptop normally, or in Safe Mode).

BTW, there's nothing at all wrong with "trying to use an 11 year old computer". I have a MacBook Pro (13", Late 2011) that is used regularly...and it performs very well for being 12 years old.