Considering photos tend to be precious and irreplaceable if lost you really need redundant backup of them to be safe. Ideally, this means at least backed up with Time Machine to an external drive locally and again to the cloud in one way or another. However, as you have just found out most of the cloud storage services just sync to local storage and do not offer a way to move the stuff off your startup drive completely. Of course, while highly recommended in general a Time Machine backup doesn't help here when what you want is to offload the stuff from the startup drive.
I would be wary of trusting any cloud solution with data I value that highly. Nothing is perfect and if they ever screw up somehow it could be really painful. So it is a lot better to have both cloud and an external drive backup to insure against loss.
I forget now but I think I bookmarked this site to check out later because they allow you to just upload stuff rather than sync it. They let you selectively do that also and other stuff but the key thing is they do allow just uploading I believe. Anyway, here's the site if you want to investigate further which I've not had time for yet:
https://www.opendrive.com/opendrive-for-mac
It's free to try it out and see how it works.
Personally, I'd like to setup something myself for certain data where I keep a backup on an external drive but also in the cloud somewhere like open drive that doesn't require it to be synced and using space on my startup drive. I still keep another external drive hooked up just for Time Machine for everything on the startup drive but for excess stuff I value but don't want on it all the time, that's the solution I hope to setup also. This would probably be ideal for you as well by the sounds of things.
Currently I do have a bunch of stuff offloaded to an external drive but I don't feel comfortable at all with it not being backed up somewhere else too and offsite via the cloud is ideal for this. After all, if somebody waltzes in here and walks off with my iMac, they will probably grab the connected devices too including the backup drives. So much for my backups, photos, rare music, etc. I have some key stuff in iCloud now but not all of it and that is nowhere near good enough considering I value this stuff. I need to get on the stick and take care of this myself.