Time Machine says it has run out of space

Today I got this error message from Time Machine on nt MacBook of early 2015:

 ‘Time Machine couldn’t complete the backup to “Syn2.local”.

   ‘The backup disk needs 118.78 GB for the backup but only 246.37 GB 

   are available.  Select a larger backup disk or make the backup smaller 

   by excluding files.’

This message is the most confusing yet in a history of failed Time Machine backups.

The facts are that the disk being backed up has only 58.04 GB on it.  Second the disk area reserved for the Time Machine backups has a quota limit of 800 GB which should be more than enough.  Third the files in this Time Machine storage area occupy 95.96 GB, according to the information on the Server holding the storage.  Fourth Time Machine itself on the System Preferences window reports  “246 GB of 816 GB available” (at least the available disk space agrees with the above area message).

The questions about all this are:

1. The above means that Time Machine thinks that (816-246) = 470 GB are occupied by stored files.  By contrast the Storage management system reports that only 96 GB are occupied by those files.  Which is right?  What might be going wrong?

2. The error massage says that 118 GB of space is required but it can’t do this because only 246 GB is available.  This is rubbish!  Again, what can this mean?

3. The storage area of 800 GB is over 13 times the data to be backed up, 58 GB.  Surely this is more than enough for everything that Time Machine has to do?

The backup server concerned is a Synology NAS, a DS416J.  Other computers here also backup to it, to separate partitions and currently are doing their backups, each with their own quota of disk space, successfully.  The net storage of the RAID system is 10.8 TB and 3.8 TB are free.  I have an ethernet adaptor plugged into the MacBook to eliminate any problems with WiFi; Time Machine only backups when power, including the Ethernet hub connection, is available.

I have run Verify on the Time Machine and no fault messages appeared.  Can I presume it is OK?

In the past with error messages such as this I have deleted the Time Machine storage and restarted it afresh.  But slowly the space gets filled up until it won’t accept any more.  Somehow Time Machine does not appear to be deleting old backups.  The Mac System Preferences for Time Machine says “The oldest backups are deleted when your disk becomes full.”  Does anyone have any idea what is happening here?