A couple of things...
Time Machine does use a case sensitive format. This is because if you were trying to backup volumes that did happen to be case sensitive, you would need a case sensitive backup. Since case sensitive is always the safe option, that's what Time Machine uses. Case insensitive formats are only a convenience for users who frequently mis-type things. Sometimes they cause problems too.
Otherwise, everything looks like it is working properly. One thing you have to remember is that the fancy, windowed user interface on your Mac is not truthful. That's just being polite, it lies to you constantly. The macOS operating system is the most complicated operating system ever made and its gets more complex every year. It is no exaggeration to say that people sometimes lose touch of reality when they start digging into the internals. I have seen that happen here on the forums many times. So, the user interface tries to give you a simplified view. By default, it hides certain locations that the average user doesn't need to see or would likely just confuse them.
If you want to learn more about those internals, you would have to start using the Terminal. Some places are even hidden from the Terminal, although there are ways to reveal them. Even then, absolutely no part of the system is documented in any way. So if you did have questions, the best anyone could do for you is educated guesses.
And to pile on a bit, Big Sur has changed the behaviour of Time Machine. If you create a new Time Machine volume on Big Sur, as you have done, then it creates it using the APFS file system using new logic. But anyone who already had a Time Machine volume has one that runs under the old HFS+ file system. Therefore, most of the people who really know how Time Machine works through years of working with it are now unfamiliar with the new system. Chances are, they are like me and still have the old version. They have never even seen the new APFS Time Machine.
By all accounts, everything seem to be working on your computer. You can double check this by following leroydouglas's instructions to "Enter Time Machine". This will display the "star field" interface. (It actually hasn't been a "star field" for years, but what else to call it?) If you can navigate backwards in time and see changes in files, and restore old versions, then everything is working properly. You can restore an old version alongside the current version. It will automatically rename the old version and you can compare differences.
