I moved photos from my MacBook Air to an external drive and lost a lot of them

You may want to check, if your external drive is compatible with Photos. If the external drive is not compatible, Photos may be opening some older library instead of your move library.

Any external drive to be used with Photos needs to be prepared as described here: Move your Photos library to save space on your Mac - Apple Support

Most important:

• The file system format needs to be MacOS Extended (Journaled) or APFS
• The drive needs a wired connection; it must not be accessed over the local network.
• The external drive must not be used for Time Machine backups.

You can see. if Photos is using the correct library, if you look at the Photos > Preferences > General. At the top of the panel the path to the library is shown.

Is the library on your external drive the system library? Perhaps after moving your accidentally used a new library to store your photos?