Just had this exact same issue.
Installed 6.2P2 (recently released) and after logging back into the vSphere Web Client, the previously hung job had errored out. I had previously been running 6.2P1.
I was in the same boat as you - VSC and SnapCenter just ddn't seem to want to "play nice" together. I spent a solid 3 days trying to crawl through every VSC log, SnapCenter log, reinstall, reconfigure, everything just short of actually restarting vCenter services. I'm sure that would have cleared the hung process, but I was bound and determined to try and figure it out to salvage the sole reason I wanted to use SnapCenter for.
Guess it's just not there yet, unfortunately. Have now completely scrapped two instances like that where I had a great use case for using Backup Policies but hopefully things get better backed in and more functionality is included to let someone perform all the same tasks from SnapCenter as they do within the VSC. It's a debate of who the functionality should reside with when it.
The root cause of my issue to begin with was somewhere along the line putting my account into the SnapCenter Admin group as a test, then before removing it, interactively having launched a backup within the vSphere Web Client.
Quirky.