Is Linux worth trying on a 2015 MacBook Air with a broken keyboard?

It's worth trying if someone actually wants to use it. Linux Mint is a reasonable starting point for browsing and office work. You can test it from a live USB before wiping the Mac, so there's no need to commit straight away.

Check Wi-Fi during the test. Some Apple hardware can need extra drivers, so having another way to get online while setting it up may help. Test the trackpad, sound and other things you care about too.

I wouldn't pay for a keyboard repair until you get a quote and compare it with the price of another used laptop. The repair can involve a lot more than swapping a few keys, and the cost may be hard to justify on an older machine.

If it will mostly sit on a desk, an inexpensive external USB or Bluetooth keyboard could make the repair unnecessary. Selling it as faulty or recycling it are sensible options if nobody wants that setup.

What kind of broken are we talking about? A few dead keys and physical damage are different problems. It may be worth checking whether cleaning or a replacement part is practical, especially if you're comfortable doing the work yourself. Get a repair estimate before buying parts, though.

You're choosing a Linux distribution rather than usually choosing a kernel on its own. The kernel is the core that comes as part of the distribution, along with the desktop and other software.

Mint, Zorin OS and Debian are all options mentioned for older hardware. I'd start with a desktop distribution you're comfortable using and stick with its supported updates rather than trying to pick a kernel version manually.