I just tried and it seems that they are indeed tied togheter.
I am not a fan of these modes, personally.
I usually just keep the phone in vibration all the time.
Nontheless I feel like this shouldn't be the correct way to manage different modes.
I think that DND and Sleep Mode should be different, and personal modes as well.
For what I can see, Sleep Mode is just another custom mode, just preset, and you can also delete it as every other custom mode.
I guess the rationale behind the current behaviour is: "This is the set of apps and users that are important to me, no matter what" and these lists are applied everywhere because they are important.
I agree that every mode should have their own list, to make sure that while gaming I can have more apps that can disturb me than when I am sleeping (or the opposite, depending on the priorities lol)
Maybe you can try to search for one app that manages notifications? I am not aware of any app in particular that can help you, but they might exist.
Quick edit: Maybe you can try NotiFilter?
You can determine what notification to dismiss and what action to take based on what notification you receive.
It also has scheduling, so I guess all things combined can be used as a new DND custom mode.