I have a 2013 “air” that was updated to 10.15 (so 64bits) ; I bought it dirt cheap secondhand for one specific app, and out of the box it did update itself when I connected it not so long ago. I changed the battery, too - most resellers include the impossible screwdrivers needed to open the strange tri-lobe screws.
If OP has a use for it, it’s not bad hardware with backlit keyboard, a decent screen, lightweight. With a new battery it’s a decent all-day workhorse. My main machines are 5th gen Intel, and I remember nothing wrong with 4th gen.
Any distro will run on it, or should. I’d bet you’ll get the spinning cube & wobbly windows easy peasy. If it’s free, just try it out.