how to back up my photos in to an external device

You have to set up iCloud photo library https://support.apple.com/en-in/HT204264

And its preferences https://support.apple.com/en-in/guide/photos/pht5156cc968/4.0/mac/10.14

Export photos from system photo library to a desired location say download folder in finder and connect an external hard drive to the Mac , then transfer the photos from download folders into the external hard drive , hence all your photo data is saved .

You can select few photos see this article Select and deselect photos in Photos on Mac - Apple Support and delete to recently deleted folder see this article Delete photos or recover deleted ones in Photos on Mac - Apple Support ( its your choice to delete them permanently immediately or after 30 days the photos will be removed from the iCloud server ) .

In this way the complete photo data is still on external hard drive , but the space is reduced in photo library .

See this article to export photos Export photos, videos, and slideshows from Photos on Mac - Apple Support

Also you have to reduce the space , not only photos occupy the space .

See some articles to reduce the data https://support.apple.com/en-in/HT204247

https://support.apple.com/en-in/guide/macbook-air/apdb468896e0/2019/mac/10.14.5

https://support.apple.com/en-in/HT206996

https://support.apple.com/en-in/guide/system-information/syspf5a64aa6/mac

One method is to copy your library to an external HD formatted OS X Extended (journaled) with ownership set to be ignored. Then delete the photos you want to remove from your library on your boot drive to free up space. It's generally recommended to maintain a minimum of 20 GB of free space on the boot drive for optimal system and application performance.

When you get new photos and want to copy them to the backup library use the paid version of PowerPhotos. It an copy albums of photos between libraries along with their metadata.

Remember, however, that you will need to backup that EHD as well as your boot drive to make sure your photos are protected.

Nomally, i will log into icloud on the browser -> choose Photo -> Select photos i wanna backup -> Click download button to down them all -> Copy to the external device you have. Done!

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Dr Pluscell