I have had this happen. Try going back offline and restarting the game, you may be able to load and save again. You can interrupt the synch without messing up your local save files, and if it's hung now it's probably going to stay hung, unfortunately.
I ended up with two options, both of which svcked: Always play fallout offline, or go into game management and wipe all my local and cloud save files for that profile and start over.
It would sit for hours trying to synch and then fail or time out. Once the cloud synch broke I never got it to work right again until it had been wiped. Microsoft decided not to let us wipe the cloud without wiping our console, and their support staff are totally useless when you go to them with this problem, suggesting things that don't work, and wasting huge amounts of your time, while pretending that this is a new problem they've never heard of, and that Bethesda can do something for you to fix it.
I hope you find a better solution, but I looked for days, scoured the net, tried everything I could think of, every suggestion I could find, and in the end I had to wipe all the save data for FO4 and start over to get past the stuck synch while connected to the net.