The MacBook Air keyboard is connected in series with a few other components:
Keyboard (w/ Power Button) —> Trackpad —> IPD Flex Cable —> Logic Board
It is certainly possible for the Trackpad or IPD Flex Cable to be faulty, causing this issue, but if the other keys work then it sounds like a keyboard issue.
That said if you could get access to a spares machine or another Trackpad and IPD Flex Cable for free or cheap, they’re at least worth a shot before stripping the entire machine down. The good old reseating connectors never hurts either.
That layout almost looks like the UK model, but without the pound symbol. Some history of the machine would be useful here, when and where it was purchased, etc. There are a lot of keyboard layouts available and I could be missing an obvious one. On the other hand it could be a standard UK keyboard with some key caps swapped over.
If you do attempt to replace the keyboard yourself, my advice is to get the entire Top Case - that is, the metal chassis of the computer with the keyboard pre-fitted. There are places online that sell just the keyboards for reasonably cheap, but the fitting process is nothing short of hell, involving removing rivets, some tapping and possibly some cutting and drilling if the rivets holding the keyboard in break.
The Top Case w/ Keyboard is more expensive than just a keyboard, but no amount of money saved would ever make me want to take on that job ever again.