It’s probably difficult for some folks to wrap their heads around Vader being the Dark Lord of the Sith whilst being subservient to a non-Sith Palpatine because since 1999, the Sith have been portrayed as apex predators who have a monopoly on dark side mastery. But this is purely an invention of the prequels.
You do realize that the fact that Vader calls Palpatine his master obviously means Palpatine was a Sith in TESB and ROTJ?
Sith was never uttered until TPM. All we know is that Palpatine is Vader’s master. It could be that they’re both part of a dark Order where Palpatine trained Vader, but we have no reason to believe Vader’s a part of any order based solely off the OT. It’s worth mentioning that Timothy Zahn wanted to name the Noghri species “Sith” to explain what “Dark Lord of the Sith” meant. Palpatine only really needs to be someone powerful in the dark side, what the Sith are and whether or not Palpatine is one of them isn’t as important.
Not that Palpatine’s relationship with Anakin should be like Snoke and Kylo Ren, but in a prequel rewrite, their relationship could be something like that. Kylo Ren is a Knight of Ren, Snoke trained him and is his master but is not a Knight of Ren. The Knights of Ren are just an order that Kylo Ren is also a part of.