We found a rather unusual solution. Although no error or warning was logged in Application Insights, a restore of our main database did the trick and solved our issue.

It could be a coincidence or not, but restarting any of the used services didn't solve the issue. Only a full restore of the db solved our problem. We never had such a problem in the past, usually if something is wrong with the db we see it in the logs or some specific requests fail, but never the whole app without any trace.