As an entity in and of itself, TOS was fully-formed by the end of the first season.I think my most controversial Star Trek opinion has to be:
Everything made before 1989 – The Original Series, The Animated Series, TNG seasons one and two, and all movies before Star Trek VI: The Undiscovered Country – are only "broad strokes canon". It more-or-less happened, ish, but specific details are not shown accurately, and problematic lines, scenes, performances, characters, effects, designs, etc can be safely ignored.
Yes, I'm afraid that means I regard Voyager and Enterprise as "more canonical" than The Original Series.
Oh – and Star Trek V: The Final Frontier never happened at all.
As far as in terms of Star Trek: The Franchise, it's a rough draft. Which is not a knock on TOS because it wasn't written or produced with a decades-spanning franchise in mind. Even the first two seasons of TNG have some wonky ideas that they did away with later. Ferengi who supposedly eat their associates, Klingons being part of the Federation, etc.
So I would have to reluctantly agree that Star Trek: The Franchise solidified itself as what it was going to be during the third season of TNG. That's why I like that DSC jumped to the 32nd Century and shook all of that off, using The Burn as a cover.