I have all my photos including many precious pics like my daughter's first birthday, etc backed up only with Google photos (as GPhotos often cleans up my phones it removes the original too).

Post like these are a true wake up call. I definitely need to setup something like syncthing to backup at least one more to good old usb 1tb drive. I guess you should too if you're in the same boat.

Make sure you get a Google Takeout, but realize that much of the image metadata is deleted (and sometimes outright changed) from the originals.

My takeout failed with an write until I requested an archive that was only photos, and only a year-subset of my library (which required me to make a manual album).

I also tried the open source "timeliner" project, (which does incremental backups very conveniently), but due to Google's API, all GPS tags are stripped from what the images that it can pull down.

If SyncThing doesn't work for you, you can also try Resilio Sync.

If you need software to manage all your photos and videos, you might want to try PhotoStructure! (I'm the author, details in my profile).

Is there a method for automatic backup of Google Photos? Something that a script could do, without manually using Google Takeout.

Also, is there another service to backup photos that doesn't modify the data? I was thinking of using Nextcloud. But the prices for Google One are quite attractive.

I run it nightly from my home server. It has a few limitations (due to limitations of the Google Photos API) but overall it does what you want.