Apologies for the confusion as I definitely could've explained it better.
For my purposes the file name is not important and I rarely ever change them. You are correct in that Plex only really cares about file tagging for proper sorting. And to be fair, the combination of MP3Tag and Plex has been excellent 99% of the time. I've been extremely happy with the setup!
But every once in a while, I come across a file or files in my collection - regardless of file type or number of files - where it simply will not put the leading zeros in the discnumber field. I can't seem to find a common denominator as to the cause. I should've highlighted it but in the example of my screenshot I was referring to how the "Uncrowned" files are "7" while the "Underlord" file is "06".
My sorting in Plex is unique in that I store multi-book series under one album that has multiple discs (where the discs are the books). If the "album" has more than 9 discs, it will place disc 10 after disc 1 when sorting hence the need for leading zeros.
It's along the same lines of sorting by track number. If you don't have leading zeroes, it can do funny things if you have a lot of tracks and sort by track number.