how to copy Photos library from an old iMac to a MacBook Air?

You could copy the photos Library from your iMac to your external drive. The drive should be prepared as described here: Move your Photos library to save space on your Mac - Apple Support

Make sure, the checkmark "Ignore ownership on this volume" is enabled. Otherwise you may have problems with the file ownership on your new Mac.

Then connect the external drive to your new Mac and drag the library to the Pictures folder.

To open it on the new Mac quit Photos, if it is running. Then double click the transferred library to open it in Photos. Check, if it readable and you are not seeing any blank thumbnails. Quit Photos and double click your main library to switch back to it.

Once the library is on your new Mac, you could import it it to your main Photos Library or just keep it separate.

Importing it will import the media (photos and videos), but not the albums and folders, also the keywords will be missing.

For a more complete merge you may want to use iCloud Photos. If yo enable iCloud Photos on your iMac and wait for the library to upload toiCloud, then enable iCloud Photos on your new Mac, the two libraries will merge in iCloud Photos , then the merged library will sync to qour two Macs. This way also the albums and folders and named faces will and keywords will be synced to both your Macs.

After getting the old library ready for transfer/import into your library on the MBA and you have lots of keywords, titles, descriptions and album in the old library you might consider using the paid version of PowerPhotos to merge the old library into the MBA library. PowerPhotos can merge more than just media files. This user tip shows the difference between PowerPhotos and Photos as far a merging is concerned: Comparison of PowerPhotos vs Photos re Importing Metadata from One Library to Another - Apple Community

Just some food for thought.