Time Machine backups not showing external HD files.

I have been using Time Machine for ever. I am using Mac mini, running Sequoia 15.7.3. I don't have any real data on my internal HD. I keep all my data that I care for, on an external 4TB HD. I have another 8TB external HD that I use for Time Machine. However, I recently discovered that, while Time Machine is backing up my internal HD perfectly, it has not been backing up my 4TB external HD. I have checked everything. The 4TB HD is NOT in the "exclude" list. So, it should be backed up. In fact, when I look at the size of the Time Machine backup drive (the 8TB external), I see that it has used 3TB of space. But, when I enter Time Machine, all I see is the folder for the 6TB HD, but nothing in it. I even took my entire setup to the Apple Store, and two techs looked at it. But, could not figure it out. I have re-formatted my Time Machine drive (as APFS case sensitive), several times. I even formatted my Mac mini and re-installed the system from fresh (not from any backups). The initial Time Machine backup took a full day (24 hours) to complete. So, it seems like it's doing something. But, still cannot see my backed up files from the external data drive.

Can anyone offer any help please? If this does not work, then I will be forced to use another software like CCC or SuperDuper. But, I really don't want to do that.

Thank you.