Check the texture compression in the Godot import settings for the texture files (you can select multiple textures at once). I find VRAM works well for desktop, but for HTML5 or Mobile you might want Lossy. There is also a bug with Godot, where embedded textures sometimes don't work. So export as glTF from Blender with glTF + textures + bin. Import that into Godot and change the compression like I said above. If that doesn't work, then remove the material from the mesh (you have to make unique and then save it first) and then reapply it as a material override on the instance. I don't know why that is needed, but Godot has problems sometimes with embedded materials.
