So, I figured out a nice import process for Godot:
1. You can just take the .glTF and the corresponding .bin files.
2. Then open the .glTF files in a text editor (they are human readable) and check which texture it needs. It will be obvious, because there is only one and it ends in .jpg/.png/.psd or similar image format extension.
Usually all the .glTF files in the same folder need the same one so it's enough to check it for a single file, but you can do a mass search (and replace) with something like Notepad++.
3. Copy that single texture from the Textures folder inside your folder containing the model files (gltf/bin) and rename it appropriately.
4. Just import it inside Godot like usual (copy it into your project).
5. Some import settings may need changing like you may need to export materials and tweak them (or reuse what's in the pack maybe?) manually (e.g. for windows), but otherwise this process works for fine.
Alternative process: they have Blender files on their Patreon and this Blender extension seems to be working fine and seems to produce glb files with the hiearchy (e.g. doors/wheels for vehicles) correctly preserved.
I have also tested the first process for their Mega Weapons Kit. Worked fine. I'm pretty sure it works for all the packs, but YMMV.
Overall, in my opinion, this is an awesome pack that's very much worth it if you're willing to put in some elbow grease when using Godot.