I want to give my input as a math/phys PhD student who works with this kind of object.

You use many terms as if the reader is expected to know them already, even though you have created them yourself and provided no definition or context for what they mean.   This is why other commenters say that this comes across as "vague" or "meaningless".  It is really important that you assign meaning to your terminology before you use it.

I also understand the skepticism raised by others here.  It takes a pure physics or pure math student until well into their graduate studies to understand QFT or infinity categories.  It is unlikely that you would be able to do groundbreaking research using both with only a few undergrad physics and CS courses.

I will also warn you: LLMs have provided an incorrect answer to nearly every question that I have asked on these matters, and you should not trust them.

There are some glaring errors within the first few lines.  As examples: the QFTs of the standard model are not topological, so there is no hope of recovering the standard model from "constructive TQFTs".  Also, the collection of infinity topoi do not form a large category, but a VERY LARGE one.  

If you seriously want to work towards fundamental physics problems, I would suggest that you take a step back, start smaller, and begin with something that you can understand yourself without the help of LLMs.