Dropbox issues with MacBook Air

That should not be necessary. Lacking any direction from Dropbox's support site, I suggest first uninstalling Dropbox. The caveat is that I have no way to determine if your missing files will miraculously reappear on your Mac or not after uninstalling it.

It stands to reason if those files are stored on Dropbox's "cloud storage" server, merely uninstalling the app should not affect them, but again I am in no position to guarantee that. Presumably you need login credentials to access Dropbox's "cloud storage" and / or to install the app, so the first order of business is to confirm those credentials are correct.

The next thing you should do — if you have not done so already — is to back up your Mac using Time Machine or its functional local (i.e. not offsite / "cloud" system) equivalent: Back up your files with Time Machine on Mac - Apple Support. Only after that can you be assured of doing anything up to and including taking the drastic and hopefully unnecessary step of "resetting" your Mac without losing its contents.

Since this is clearly a Dropbox related concern, you are almost certain to find more competent assistance on its Community Forum, here: https://www.dropboxforum.com/t5/English/ct-p/English. I can help with using your Mac, but not so much with using third party programs like it.

Nevertheless if I find an appropriate similar concern on that forum that seems applicable and was resolved in a manner that makes sense to me, I'll let you know.

Update: This appears to be relevant: When I any file on my Mac it goes to ~/Library/CloudStorage/Dropbox/.Trash instead of ~/.Trash

Jumping to the end seems to conclude updating macOS fixed it...?

This Dropbox help page explains,

If you’d like your files saved on a computer’s hard drive (or multiple computers’ hard drives), as well as to your Dropbox account online, you can choose to do so when you download the Dropbox desktop app. When prompted, choose “available offline” instead of “online-only”.

(emphasis added)

https://help.dropbox.com/sync/sync-overview

Perhaps you chose "online-only"?

That is the extent of my knowledge though, and that page does not explain how to revert that selection. For more extensive help you will need to contact that product's developer: https://www.dropbox.com/support

That help page is less than satisfactory for a number of reasons. Downloading an app does nothing. Launching it for the first time probably asks some configuration questions, which is understandable, but it does not explain how revert that configuration. Maybe it's impossible? The next thing I might be tempted to do is to uninstall the app, but then who knows where your documents went or if you can even get them back.

Yes it's a right mess.

When you save a file, is that the location suggested by the usual macOS "File Save" dialog? If so you ought to be able to simply select some other location, such as Desktop or Documents.

The reason for asking is that I don't have the Dropbox app installed. I have used it, but only through its web interface.

What a mess. I'll keep it in mind should I ever be tempted to install Dropbox.

Thanks for the update.