The issue was resolved. The problem was that the object storage system unexpectedly stopped sending notifications to our application about completed uploads. By this uploads were stuck in the "waiting" status.
Unfortunately, our monitoring was not able to detect this issue. As this happened in the middle of the night in our timezone, we unfortunately were not notified about this issue and the automatic status page did not show this issue. We will improve our monitoring system to detect such issues better to be able to react more timely.
We are very sorry for any inconvenience caused by this issue.