First person shooter game

do you know any good tool to convert animated FBX to GLB?

Unfortunately no, I haven’t found definite solutions about that, as I’m going to make my own models and animations in Blender. From what I’ve seen, it’s a hit-and-miss, unless you own a couple of the (very) expensive 3D software like 3D Studio Max, Autodesk, Maya, and even then you have to find the optimum path to three.js. I’ve done this in the past using trial versions.

Blender’s fbx importer is far from perfect. I tried to import your main character file (mutant.fbx) that is just the mesh, then I imported the walking animation file (mutant walking.fbx) which was bones + animation, and appeared …a tiny skeleton inside his foot. I enlarged it (s + mouse) but it needs to be applied to the mesh in order to control it (which might range from easy, to a lot of work), as when I pressed “space” the bones started moving …without the body.
Then you need to assign the textures one-by-one using nodes, etc (BTW I’m always using exclusively “glTF Metalic Roughness” instead of the default “Principled BSDF” that needs to be downloaded separately, to ensure compatibility with three.js).
In other words, it might be feasible by investing considerable time, but it might also be time consuming, especially if you have many models.

EDIT: Not sure if you can have (or if it’s efficient to have) separate glb bones-animation-only files. If that’s feasible, then you only have to apply the textures properly to the main mesh, which is not a lot of work.

Alternatively, there is a commercial importer for Blender called “Better FBX Importer & Exporter” ($25) that supports importing animated fbx models, but I don’t know any details, although there is plenty of info on the author’s website.

Alternative #2: perhaps it is feasible to export animated gltf models from three.js - as discussed here Exporting Model with animations?