Like others mentioned, request Google Takeout which gives you all your photos. I recommend keeping the original zip/tar.gz for future reference (e.g. you need specific metadata not included in the photos directly).

Also, make sure to keep backups. E.g. upload it preferably encrypted, and store the password in a password manager. Make a copy on a USB SSD, and not just the Steam Deck (you might wipe it, lose it, …).

If it is generally possible with a browser it is possible on the Steam Deck.

Boot to desktop mode.

• Download your photo cloud to your phone, and send them over USB or Bluetooth or KDE Connect. make sure firewall for kde-connect is checked to allow.
• Use browser to visit GPhotos?
• Can also try using KDE Kio GDrive or Google Takeout to integrate Google into Plasma or physical download options.
• Or be crazy and try Waydroid and installing Google Photos there.

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Very very easy to do with a Steam Deck. Let me know if you need directives.