What is causing these material changes?

For the most part, the problem you are experiencing is related to the shader nodes and textures you are using and the combinations that you make for a given shader.

In order for Blender’s viewport to look as close to Verge3d as possible you have to be sure you are using the shader nodes as expected by Verge3d. Verge3D supports many nodes but also leaves out certain properties that have a major impact on what you see in Blender and what you see in Verge3d.

The Normal Map Node is one of these. You have your normal map node set to Object Space…this will make the objects look different for sure. The only mode that is supported is Tangent Space. So you will want to change all of those and make adjustments as needed.
https://www.soft8soft.com/docs/manual/en/blender/Shader-Nodes-Reference.html#Normal_Map

The other issue is you are using a Color Node in your World Shader. According to the documentation, there is no support for the Color Node in V3D. See link below for supported nodes.
https://www.soft8soft.com/docs/manual/en/blender/Shader-Nodes-Reference.html

I think if you go through all your shader nodes and validate you are using only supported nodes you will be much closer than you are now. As an experiment, you can disconnect your image texture and color node from the World shader and things get a lot closer, and when you turn your Normal Maps to Tangent Space it’s even better.

I believe I may have commented on this before…but this is very detailed both in texture size and polygon count for this sort of hard surface model. If your plan is to just brute force this into an Electron app….then disregard the following. If your intention is to release it as a web app…you need to heavily optimize your file. This optimization is going to cause you to have to redo your UV’s more than likely so I would spend time doing some of that heavy lifting now and then rework your shaders once you have new models as those will need to be reduced so they are not so heavy too. Just my two cents. Good luck…looks like a fun project.

Hmmm. I am going to have to give this some thought. What is the deliverable to the client? If its just to get them something to look at, a video would be much easier. If it’s something to interact with on a PC as an electron app then your approach will yield large files but if it’s free.
However, this current approach is not going to be well suited for web or mobile use.

STL files are great for CAD. Not great for Webgl. Your current scene is nearing 1,000,000 triangles. Retopologized it would be closer to 100,000. Since you are going to want to output these quickly you are not going to spend time making the geo optimized…and you want to use some sort of automatic UV. Given you are using mostly metals. I would think that would be fine. No stickers, no real textures. You may want to use Verge3D material pak and just use those. It will simplify your mats.

Now to answer the question. There are no shortcuts to good geo, good UVs, and good shaders that provide a good experience. There are simple approaches for quick things but you are going to limit the devices that can view your app and you are going to be stuck fighting the Blender Viewport vs the Verge3D rendered view.

If quick and simple is the approach you need – go video. If interactivity is what you need, then the price to pay is a lot more time to make your projects look like video quality while using 1/10th or less the model and texture sizes.

While on textures sizes….stick to “power of two” textures sizes. You need all the efficiency gains you can get.