Is there a way on Linux to backup the photos to the computer without using a cloud service?

Yes! There is an OSS implementation of (parts of) the proprietary protocol for USB communication to iTunes so you can indeed get your photos. I say parts because some functionality is not implemented, like the offline backups feature.

https://wiki.archlinux.org/title/IOS

Thanks for the link. Looks like I won't need macOS at all! :-)

Note though that with only one apple device, you won't have access to to icloud if your device is stolen or you get locked out because you forgot your pin or similar. If I log in to icloud on my laptop, I first have to confirm it on a linked device... as i only own one device if that device is linked I can't use Find My or similar. See also: https://news.ycombinator.com/item?id=34407087

Any suggestions for calendar syncing? It's basically the only thing I use iCloud for.

Would like to avoid Google and don't mind running my own server to manage it so long as I can use the default calendar app on iOS.

You can run owncloud and use their app to automatically upload photos and videos in the background.