Total lack of consideration of Einstein's theory of relativity

The warp field generated by the dilithium crystals keeps the ship in temporal sync with the rest of the universe by creating a static chronometric effect which is then routed through the tachyon amplifier to displace the space-time continuum inversion. Obviously.

It's just a TV show

There is actually a considerable amount of speculative science behind the Warp Drive that works around Einstein's theories. The Warp Drive from Star Trek is actually very similar to the theoretical Alcubierre "warp" drive:
https://phys.org/news/2017-01-alcubierre-warp.html

With this type of warp drive, the vehicle in which a user is traveling is actually not moving; instead, the drive on the ship warps space in front of and behind the ship (hence the name "warp drive") and then rides this "wave" or "bubble" much like a surfer rides an ocean wave.

Since the ship itself is not moving, and only space around the ship is moving, the ship does not experience the relativistic effects we would experience with normal forms of propulsion.

In any form, the explanation for this type of FTL travel has always been that those inside a starship's protective "warp bubble" are protected from the relativistic distortion of time known as the Tau Effect. And, while not specifically mentioned in the show, I believe that most of the technical manuals mention that the maximum sub-light speeds of starships only approaches about 0.5 C, so that would minimize any distortion of time due to the Tau Effect.

I'm afraid your premise is wrong.

By its own definition, the model defined in Einstein's theory of relativity establishes that time slows down the closer you are from the speed of light, and that you can't exceed that limit. The case 'faster than light' is out of theoretical bounds, it's just considered impossible in that framework. By its own definition, when it comes to travel faster than light, the Einsteinian model can't be applied, the same way right now Newtonian model is the wrong model when you travel close to the speed of light (or you you don't, but you require high precision calculation).

If 'faster than light' travel is possible, you will need a new theory, a theoretical framework that probably will include Eisntenian mechanics as a particular case.

https://www.youtube.com/watch?v=8VWLjhJBCp0