That's a loaded question. Short answer: no.

Longer answer:

would it possible to extend the VRAM for example (even if it looks and implement in a hacky way) with these extra components?

For VRAM, it is possible. It requires specialized tools. There are hundreds of solder balls on those chips, this requires machines meant for it and can't be done without the proper equipment. In addition, every time you de-solder and solder new memory, there are risks of the chips not being perfectly aligned and that will cause issues. You also have to make sure the memory chips are of the right type for the GPU (the actual chip, the entire assembly is a video card even if we often refer to it as a GPU) to handle it. That means that not all memory chip may work. The card uses Micron GDDR6, better use Micron GDDR6. That leaves you with basically using chips of the same generation with higher capacity.

Finally, the vBIOS may need some modding to work properly. That's involved, but it's doable and has been done before.

Now, assuming all that is covered, there is the issue of whether the GPU can handle the extra memory. That's where the bus width comes in. Think of the memory capacity as the overall number of cars you can fit on a road. The memory bus is the number of lanes on that road. If the bus is too small (lower number of bits), you won't be able transfer data to and from the VRAM to take advantage of extra capacity. For a current example of this, look no further than the 4060 Ti 8 GB and the 4060 Ti 16 GB. It's not quite to the point where the 16 GB variant can't take advantage of the VRAM in some cases, but there's a reason most reviewers says the 16 GB variant is bad value.

I've always thought it's such a waste to chuck away a GPU just because some components of it doesn't work. I also thought that imagine you take many GPUs apart, build one gigantic circuit in a room, one cabinet is filled with memory chips, a another is filled with processing chips, abother cabinet with other components and all is connected via cables and such leading to the computer.

That's a big fat nope. If you ever look at a video card PCB, you'll notice the VRAM chips are extremely close to the actual GPU die. There is a reason for this. Basically, the farther from the GPU die the VRAM is, the more signal degradation there is and the more latency there is. Signal degradation is an issue considering the clock speeds at which VRAM works. Latency is pretty much self explanatory. There actually used to be swappable VRAM chips on ancient video cards, they went the way of the dodo due to the issues I mentioned.

That's one issue, another is that PCB design isn't simple, especially if you have something as complex as a graphics card, let alone a PCB with more than one GPU on it.

What you're describing is a bit like computing clusters work. The main difference is that each cabinet has racks that contain CPUs, RAM, etc. or a bunch of video cards in the same rack. The interconnect speed between the racks and cabinets is already a concern and often these need not be as fast as the RAM channels, etc. By the way, this was already a concern 20 years ago.