the part i think youre missing is that "survival of the fitness" is shown elsewhere, and used as a tool here to identify what the fitness is, and how and when certain traits were beneficial.
the case you are descibing is that all applicatioms of science(well, of anything) are circular reasoning. if you use newton's mechanics to predict motion of a mass undergoing acceleration, its circular because your result is proof of newtons mechanics, and newtons mechanics is proof of your result.
its just an "if and only if" relationship. that's not circular reasoning.
Also you don’t understand physics, the proof is that you can make predictions and then verify the results.
In the end evolution is random, but exerts some pressure towards fitness in some environments. Some traits are legacy or are just plain random; just because an organism has a trait does not mean it is useful now, or indeed has ever been useful for fitness. The whole package must be reasonably fit for some environment, but that doesn’t mean all the traits improve fitness.
Again, I gave numerous examples, and you ignored mostly all of them.
Just to develop the point about extinctions a bit further. We know for instance of birds that had no natural fear of predators on the Galapagos Islands that upon human contact were driven to extinction or near extinction, and we don't need any circular assumptions to tie their fitness to their extinction.
And that's not to mention the rest of the examples I listed that you ignored, such as cases where we can observe that currently living species are doing well or poorly, like algae and pandas respectively, all of which hinge on knowledge of specific biological mechanisms.
So I don't know why you keep asserting that it's an assumption.
No, logically it is proved true because it is assumed to be true and then used to prove itself.
> For starters, species go extinct all the time for reasons tied to their evolutionary trajectory.
Again, this is circular logic. You assumed that the only reason that species go extinct is because it wasn’t fit enough. If you assume survival of the fittest then of course it is true.
Here’s another circular explanation: things are the way they are because God created it that way. This explanation rises to the top precisely because it has explanatory power all across nature without evident counter-example, right?