Is it safe to clear the 'Library/Caches' folder for disk space on my MacBook Air?

I wouldn't. There's an awful lot of stuff in the Caches folder that affects many things. In the big scheme that Caches folder is not especially large. For example, deleting that folder on my Mac would only gain me about 2.6 GB of storage.

If you're serious about freeing up space you should consider using an external drive and offloading your user libraries and files that don't need to reside on the internal drive. Apple has great guidance for that here: Free up storage space on Mac - Apple Support

Files that take up the most room are movies, images and music, as well as app installers and anything else downloaded from the internet. Remember, if you downloaded it from the internet it doesn't need to live on your Mac; you can always download it again when/if you need to.

Among other tasks, booting "Safe Mode" will remove certain cache files maintained by the system: Start up your Mac in safe mode - Apple Support. Do that and then restart your Mac normally. It is unlikely it will result in reclaiming any appreciable disk space, but it is harmless.

Unfortunately, my friend, you're learning that 256 GBs of storage your MBA has is not quite enough to carry you forward. Hindsight is 20/20, but I'd never recommend that minimum configuration to anyone.

Ideally, you want to be able to have a minimum of 10%-15% of the total storage capacity available at all times. With that 256 GB drive, that would be ~25-40 GB. This allows the OS to work efficiently. Too little free space and sometime a Mac will even refuse to boot.

I recommend you first take advantage of Time Machine and create a backup of your stuff on another external drive volume. For a TM backup you'll want an external drive that is 2x-3x the total capacity of the startup drive. Create a backup and then you can go about deleting files from your startup drive until you have a comfortable margin.

Back up your Mac with Time Machine - Apple Support

Also, if you aren't already using iCloud storage, then you might consider doing that. Apple has already provided you with 5 GB of storage to take advantage of. If you need more the cost is relatively low. Please note that iCloud is not designed as a backup media for the Mac.

What you can do with iCloud storage - Apple Support

Manage iCloud storage on Mac - Apple Support