Do you only want to backup the media files or the complete Photos Library?
- If you just want a backup of the media (photos, videos), connect the external drive, open Photos, and export the photos and videos from Photos. Select large batches of Photos at once in Photos, but not more than 1000 items or so at once, then use the command "File > export > Export unmodified originals". I would use the option "Folder name: Moment", so the photos taken at the same day at the same location will be saved to folders named with the date and the location. Export the edited versions as well with "File > export > Export Photos". set the filter to show only edited versions for this second export.
- If you want to backup the complete library, that is really tricky, if the internal disk of your MacBook Pro is not large enough to hold your complete Photos Library and you are forced to use "Optimize Mac Storage" for your Photos Library. If you are keeping your photos in iCloud and the library is optimized, your local copy of the library is incomplete, because many of the high resolution originals will be only in iCloud. And if you just copy the library to your external drive it will be incomplete and does not suffice as a backup.
- So you will have to turn off "optimize Mac Storage" for Photos, and wait for the originals to download, then copy the library to the external volume. And this will simply not work, if your Mac has not enough storage on the internal drive.
- So you have to start with a new, empty Photos Library on the external drive (Create additional photo libraries in Photos on Mac – Apple Support (UK)).
- Make the library on the external drive your System Photos Library and turn on "iCloud Photos" and "Download Originals". Once the download is complete, you have a backup copy of your optimized library on the external drive.
Only, this is also not feasible, if you are not very very patient. The download can take several days, even weeks, if the library is large. While your iCloud Photos Library is downloading to the external volume, you will no longer be able to use the iCloud Photos library on your internal drive, because only one library at a time can be your iCloud Photos Library, and turning on iCloud for the library on the external will have disabled iCloud Photos for the library on the internal disk. And you will have to sync your main iCloud Photos Library on the internal again with iCloud, once the backup has finished. Having to switch between two different local libraries and making them the system Photos Library and iCloud Photos Library in turn is horribly wasteful or a large library, as the upload will have to start over again and again.
The best way to continually backup of your iCloud Photos Library on an external volume, if you have to use optimize storage for iCloud Photos, is to make the backup from a different user account. Create a second user account using the same iCloud Apple ID, then create the Photos Library on the external drive and set it up as the iCloud Photos Library for this account, without "Optimize Storage".
Only this way you sync two different local versions of your iCloud Photos Library with iCloud Photos, without having to toggle iCloud Photos on and off again between the your main Photos Library on the internal drive and the backup library on the external. I outlined this procedure in this user tip: How to back up an optimized iCloud Photos Library - Apple Community
BTW, the external drive you are using should be prepared as described here: Move your Photos library to save space on your Mac - Apple Support
And it should always be connected, before you log into the user account, where your are using this Photos Library.
