MacOS – How to Disable Airport Sniffing

what you want to do is setup your express to be a "bridge" for your airport extreme network, you want to create a "new" wireless network (but if you use the same settings as your extreme, most macs should seamlessly work and switch as required)

make sure your airport express is configured not to do any NAT or give out IP's as that is maybe what is conflicting with your network currently, also make sure you give it an IP in the same subnet as your airport extreme and also that it does not conflict with any other machines

Bluetooth and WiFi do use the same 2.4GHz¹ frequency bands (as do many other things), so they could interfere relatively easily. It also doesn't help that there are a lot of networks in your area. However, I find it highly unlikely that the interference would cause you to lose your connection, given that the video shows a full 4 bars when you are connected.

Personally, I would suspect a hardware issue in this case. The Bluetooth and WiFi connections are most likely controlled by the same chip in your computer, so it may be malfunctioning only if both of its services are being used. Try reproducing the issue on someone else's wireless network, and take it in to an Apple Store if you can. If you cannot reproduce it on someone else's network, it may be that your router is picky with its connections, or something else completely.

¹ 802.11n does allow using a 5GHz band instead, so you could try that if your router and computer support it. It isn't very commonly used yet, so there is typically little interference there.