How do I backup all my photos from my Lightroom Cloud to a local drive on my Mac?

You could 'Store A Copy Off All Originals' and select the location.

This will MIRROR the contents of the Cloud, so the External HD would need another space to cover this.

(Note: I you delete a photo from the Cloud, it will delete on the External HD too. It's a mirror for direct access, not a back up).

On return from travels you can let sync commence and the ant new photos will upload to the Cloud.

Here is a video that may be of interest:

https://youtu.be/uJESj9UsS8o?si=5oSD6gLrcqrs2wSi

2 options:

1. Lightroom Downloader: https://lightroom.adobe.com/lightroom-downloader

2. You can use Lightroom Classic to sync all your albums from Lightroom. I'm using this options, to continue editing on Classic for features that are missing in CC.
By default, it downloads it into a "kind of "zip file.
Either move manually each album into an external drive, organizing the folders as you wish (based on your albums), or change the settings in Preferences > Lightroom Sync > Location, to automatically sync the photos in a specific location. You can either sync directly to your external drive, but you will need to have it always plugged when starting Lightroom Classic. Or just move them after the sync to the external drive (within Classic)