Congrats on the nice connection!
At those speeds, your internet connection is going to be faster than most devices on your network. The most common ethernet speeds are 1Gbps, 2.5Gbps, and 10Gbps.
The technician's laptop likely had a 10Gbps ethernet interface, which is why he was able to get 3.5gbps on his testing. Your gaming PC likely has a 2.5Gbps ethernet interface (hence why it is topping out at 2.3Gbps), and your older PC likely has a 1Gbps ethernet interface.
Make sure your router can support 10Gbps, then upgrade your Ethernet cards accordingly in each PC. Also, when running a 10Gbps network, CAT6 cables are recommended and rated for those speeds (CAT5e cables can reach those speeds too, but only at shorter distances and they are not officially rated for 10Gbps).