Knife Tool is stuck to the origin of the geometry of the object The Knife tool is stuck to the origin of the object. I hover all over the vertices and edges, and nothing. There is nothing inside of that object, no hidden vertex, it's literally the origin.
I tried it on all of my objects in the file, and they all have the same problem, but when I open a new file, the Knife Tool works just fine. I can't find the answer anywhere else, so the only way to continue is to copy paste everything I have in that Blender file to a new one in order for it to work again.

System Information

Operating system: Windows-10-10.0.19041-SP0 64 Bits
Graphics card: GeForce GTX 1060/PCIe/SSE2 NVIDIA Corporation 4.5.0 NVIDIA 457.30

I am using Blender Version 2.91
Your View clipping range in the 3D View in the 'bad' file, is enormous, so the depth calculation for point-picking in the viewport is beyond floating-point resolution.
In the 'View' tab of the N sidebar, set the Clip Start and Clip End to values that are enough to comfortably accommodate your scene, but no more.
A visual clue that this is happening is 'shards' appearing in shaded surfaces, like Z-fighting, even though the surfaces interfering with one another are not coincident.