I never used MJ14 so I don't know why it isn't showing the "Playlist Format" option for your hard drive, but I don't think it would be based on size. I suspect it would be based on whether the HDD was seen as a removable drive when it was plugged into the PC that MJ14 runs on. You can check that by connecting the HDD to the PC and checking the HDD properties in Device Manager. If you populate the fields on the Volume tab of Properties. Is the Type set to Removable? It should also show "Policies > Quick Removal" set to disable write caching, so that the drive can be quickly removed without loss of data.
Basically, a USB thumb, SD and MicroSD cards would always be seen as removable media, while HDD may not. Although a USB HDD should be seen as removable.
I suspect that the TV takes a while to load the music because it is reading all the Cover Art from the files, for the nice display you like. It needs to read every file to do that, and I doubt it caches that information between power cycles. If the TV only goes into standby I would hope that it did remember everything and quickly display the Cover Art again, but on an Android TV such as that, what you are seeing is an App running on the TV. If you played music, then watch some TV, you would have switched Apps, so the TV wouldn't remember all that art. It would have to re-read them again. But your Adata S102pro 64gb USB thumb drive is supposed to support 100MB/s read speed, so it should be as fast as your Adata Nobility NH!3 500GB HDD. I don't know why the thumb drive takes a while to load your music and the HDD does take long. Strange.
Anyway, I could write a book on your options going forward. But I think there is a simple solution for you, without upgrading to MC25 or buying anything new:
Copy the contents of your S102pro 64gb USB thumb drive onto your Adata Nobility NH!3 500GB. Make sure that the directory structure is identical. i.e. If the music is all under \[Artist]\[Album]\ directories, and the Playlists are in the \Playlists\ directory of the root directory, they need to be in exactly the same structure on the HDD.
Then plug the HDD into your SONY XBR-65X900E TV and test. Because the HDD is faster than the USB drive, your music should load fast. Because you are using the exact same directory structure and files that the USB drive had, your Playlists should be found and loaded.
Let us know if that works for you.
PS: I don't know your level of PC skills, but all the issues with Playlists could probably be fixed by editing the Playlists saved to the HDD and USB drive to point to the correct location. I'm pretty sure that there would be Playlist files on both the HDD and USB drive, if you looked using a PC. Playlists usually only show up as existing, but empty, when they are pointing to the wrong location. As I said earlier, that can happen when HDD drive letters change and Playlist point to absolute file locations, including the drive letter. The hard part in fixing the problem that way is knowing what the Receiver and TV expect. Your TV, like mine (equivalent to a Sony XBR 65X930D), doesn't provide a lot of information about that in the manual. Although Sony could probably help.
PPS: I loaded up a small amount of music onto a USB thumb drive, and plugged it into my Sony TV. There was a very slight delay, but it loaded pretty quickly. As with you, artwork and Playlists showed up and worked. When I turned off the TV, which really means putting it into Standby, then turned it back on again the music and Cover Art was still there. I didn't see the slight delay I saw earlier. Your TV is a later model than mine, so should work at least as well. Maybe if I loaded a whole lots more music onto the drive I would see the delay you are seeing.