[Fnoord]

Try to get the screen or battery replaced. To be fair, they're easier user serviceable than newer MB(A/P)s. For example, me with my MBP 2015 will have a harder time to service it once it gets EOL (hardware-wise) than you have now with your MBA 2012.

[fluffything]

I've replaced the battery twice, last time in september 2019, and this last time it costed me 60 EUR, and the battery life is much better than the original one.

I might want to replace the battery again in the next 3-4 years if I still have this laptop, and you might be right in that this might not be possible, but at least today it is.

[Fnoord]

Oh it is likely possible via iFixit or other aftermarket. Just not officially via Apple.

[fluffything]

Yep, I just googled my model + battery, and ordered a new battery from iFixit. Took like 15 min to swap the battery myself.