Despite being dark side Force users and Darth Vader’s followers, the Inquisitors aren’t Sith Lords in Star Wars, and the reason is due to the Sith Order’s complicated restrictions. Star Wars is a complicated series with hundreds, if not thousands, of contradictory storylines and retcons, but such small concerns pale in compared to the plethora of regulations that members of various groups and orders — the Sith being one of them — must adhere to.
The Sith, like the Jedi, follow an ancient religion centered on the Force, but their focus is on power, passion, and surrendering to the dark side. But just because someone uses a red-bladed lightsaber and pursues the dark side of the Force doesn’t make them a Sith. In Star Wars, anyone can use a lightsaber; it is not necessary to be Force-sensitive, but being a Jedi requires devotion to the Jedi Code. In a same vein, becoming a Sith entails abiding by both the Sith Code and the Rule of Two.
Following the Jedi Purge in Star Wars canon, Emperor Palpatine carried out his plan to form the Inquisitorius, a group of dark side Force users tasked with tracking down any Jedi who managed to escape Order 66. The Grand Inquisitor, a former Jedi Temple Guard, was in charge of the group, which was led by Darth Vader. Because they operate outside of the Rule of Two, the Inquisitors are Sith agents rather than Sith themselves.
If the Inquisitors existed during the Old Republic, when the Sith Order numbered in the thousands, it’s plausible that they would have become Sith. In the Age of the Empire, only Palpatine and Vader were Sith Lords; hence things were different. In many aspects, the Grand Inquisitor is similar to Ahsoka Tano, a former Jedi who continued to wield the Force and her lightsabers while not being a member of a certain order.
It’s worth noting that while most Star Wars films, TV series, and games included dark side Force users, the majority of them were not Sith. Darth Maul, Count Dooku, Darth Sidious, and Darth Vader were the only Sith Lords in the major films. However, Maul was no longer a Sith when Sidious apprenticed Count Dooku, and despite dominating the First Order, neither Snoke or Kylo Ren were Smith. The Sith have remained as elusive as leaders as they have been in the shadows, and the Obi-Wan Kenobi trilogy will be no exception.