The problem we have here fundamentally is this. At present, what we see is that you have moved to 4.x from 3.x and there are background tasks on your 4.x platform now finishing converting the 3.x data. We know this however only from what you have said.
The reason we know this only from what you have stated is because you dont wish to give access to the installation. This is, of course, your choice. However tickets will go back and forth and information will be lost in communcation when we cant physically see what we are dealing with unfortunately. And there will come a point where its stated "We cannot assist any longer" due to this. Much in the same way as you asking questions of a mechanic, not wanting him/her to see your car. The end result would at times be "Sorry, I'd really need to see the car".
You also appear to be checking some items in the database and assuming them to be incorrect. For example the base url part. That may actually not be incorrect at all in the way the data is stored, as we need to account for when sites are moved and the URL changes. Unless you are 100% sure about something in the database, you really shouldnt be trying to interpret that.
In answer to the question there, anything relating to 3.x upgrade is no longer supported and hasnt been for quite some time. So until the data is migrated, and rebuilt (I believe this is the part you are missing) we are unable to support.