I watched umbrella academy and thought the exact same thing about the TVA. I do wonder if they will explain why they have that aesthetic, as they do seem to cover as many bases as possible when it comes to explanations in the MCU. I also wondered if they have separate divisions for different planets? as everyone looks human, and they only seem to deal with the timeline as is pertains to earth.
With Loki himself its like the kind of fast tracked him into being the Loki we knew that died in Infinity War. It did surprise me that he saw his 'future' death so soon in the show, although looking back it was a good way I guess of getting casual viewers up to speed quickly who may not have seen all the films / may want to make them go back and watch them.
I wont go into theorising too much on Loki, as to be honest there millions of different things you can talk about, I want to enjoy it as it is. I think the strengths it has at the moment are the cool aesthetic and weird vibes of the TVA (always an MCU strength when they go for more kooky and weird stuff more like Ragnarok did), the chemistry between Owen Wilson and Tom Hiddleston and the fact that you don't really know the intentions of any of the characters, even Loki himself, making it difficult to know where the plot is going.
I will say though that it seems it will have the most impact on the MCU out of the three shows so far.