storage on MacBook Air

What's going on is that recent macOS versions made what used to be a simple determination of available disk space inscrutable. The theory is that if you need space for a large file you need to download (a movie or a macOS upgrade, for example) the system will make it available to the extent possible. It does that by identifying storage space that is "purgeable" and purging it. The videos you deleted should fall into that category.

For now read See used and available storage space on your Mac - Apple Support. Pay particular attention to the description of System Data. It means what it says, every word. Continue below, where it says (emphasis added):

"The remaining space is free storage space. Free storage space is physically open space on a disk. Available storage space includes free storage space and purgeable disk caches (disk space might be both available and used at the same time)."

Wait, what? Disk space might be both available and used at the same time? Is that supposed to describe Schrödinger's cat's litter box or something? Yes, I suppose it does.

Then, if you still need to reclaim space, read and follow Free up storage space on your Mac - Apple Support. Let me know how it goes.

Yes it is. The more you delete the less space you have. Soon, your disk will be completely full of nothing.

First please be sure you are using Time Machine: Back up your files with Time Machine on Mac - Apple Support. That just goes without saying (and read below).

Next: Are you actually unable to copy or download something due to lack of space?

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For an illustration of how bizarre this subject can be, read "About my Mac" and "Disk Utility" show vastly different disk storage - Apple Community. It won't make things any less crazy, but it may help show that Time Machine can be a factor.

For now I would avoid burdening yourself with concern about it. I would become concerned if you needed to download something, and found you could not due to lack of space.

Apple has been their usual tight-lipped self on the subject and has yet to explain the way it works to anyone's satisfaction. Reasons are likely to involve maintaining IP security regarding their highly proprietary Apple File System, and the fact they want the flexibility to change things at their whim without having to explain or justify their decisions to anyone. They do that a lot. It has also become apparent they consider unused system resources (such as memory and storage) wasted resources. So it's not surprising that if you have a lot of storage, macOS is going to use it.

Of course users must always have control of the storage they paid for, so if you need it, your needs should come first. There will always be some "free storage space" (to use Apple terminology) but they don't discuss just how much that is. In the past, they hinted at a value expressed in xx GB or yy% free space, but those documents have been removed. Today, the only hint is that occupied space becomes relinquished when it is "needed for other things": About Time Machine local snapshots - Apple Support.

I still need to get a good external drive to start using Time Machine. I'd rather not leave it hooked to the MacBook all the time. I can just connect it once a week for the backup, yes?

Yes. While it waits for that backup disk to be connected, TM will continue to back up using its own source volume as a temporary destination. It's perfectly ok to connect a backup disk every once in a while, because those "local snapshots" are real, completely restorable system backups. The obvious concern is that the startup disk or the entire Mac might suffer a catastrophic failure. Recovering from such a catastrophic event would require restoring an external backup.

Instead of worrying about diminishing free space on the MacBook internal drive, consider a small external drive. You can get a superfast 1 gigabyte SSD for about $110. I have a Samsung T7 which is about the size of a stack of 3 credit cards.