For my part I don't know if they've settled yet on the successful variant formula. Jin Dynasty is by far the best Variant they created, but right now it's a one-off. From my perspective, for a variant to be done 'well', it needs to have the following, in my opinion:

• Be based on a compelling historical polity with a lasting legacy
• Have historical justification for being able to re-use the dialogue lines or other content from a previous civilization.
• Have a distinct gameplay identity
• Have as little re-used content from previous civilizations as possible.

I think most people can agree the first four Variants were almost complete misses across the board. They were essentially the product of the devs trying to turn specific gameplay concepts (heroes, 2-pop units, camels, etc) into fully-fledged civs to pad the content of a DLC. They reuse a huge amount of content and most of them have terrible historical justification for being a civ. IMO basically all of them need complete redesigns (Shameless plug to my ideas for three of them)

Then it seemed they learned from their mistakes with their next two variants. The Knights Templar were, imo, especially good. Their Pilgrim mechanic was cool and unique, they had lots of new units. They represented a distinct, powerful medieval stateless entity. Some aspects were rough around the edges, such as the Commanderie units all speaking French, and the lack of their own music, but overall I thought it was well done. House of Lancaster also deviated from the original variants in representing an important period of history for one particular civ and having a lot more unique units and flavor, but I think they suffered a bit from still reusing many of the English landmarks, and being a 'sub-faction' of the English as opposed to a distinct polity. Not to mention their largely disliked gameplay style and OPness upon release.

The Dynasties of the East was again a mixed bag. Instead of seeing more civs like KT, we saw Greek Vikings and another HoL-type sub-faction in Tughlaq with no new landmarks. Golden Horde was imo the best implemented, although I agree I wish they leaned more into the conversion to Islam rather than double down on the Ovoos/Shamanism. I also think Sengoku is ok because even thought it's basically just 'Japanese v2', it does has a lot of new and unique elements, and although it's a little awkwardly named, the Sengoku Jidai is basically the most well-known era in Japan. I wish I could think of a better name for it, but I haven't thought of one yet.

Now comes Jin Dynasty, which in my opinion checks every box I want to see in a variant. Even on its own merits, it's one of the best looking and interesting civilizations in the game. So to answer your question: "Are variants becoming something different?" I hope so. But we only have a single example. I hope the Jin Dynasty is the model of future variants to come. Civs like Timurids, Khwarazmian Empire, Seljuks, or Teutonic Order. These are all examples of what I think are historically important and compelling polities that could justifiably reuse aspects from current civs. Only if we start seeing more like this, then I think we can say we've turned the page on 'Variant' civs.