Also, as for Palpatine and Vader’s use of the Sith? I tend to think of Palpatine as somebody who used the Sith as a means to an end, while Vader fully embraced the ways of the Sith. A grifter vs a true believer, as some would say.
In my personal headcanon, I’ve smooshed the Palpatine and Darth Bane characters together. I imagine he had many of the same epiphanies the Bane of Legends/canon did. He may’ve even adopted the Rule of Two at some point. But that went out the window once he discovered how to escape physical death by transferring his soul into other bodies. At that point, any prospective apprentice became a spare body rather than an heir to the Sith legacy. Like the Jedi, the Sith believe in “passing on what one has learned”, but Palpatine would horde his knowledge, and this is anathema to the Sith. Another reason for acrimony between the two parties.