How small can turbojet engines be made whilst remaining fuel efficient, light, cheap, and producing enough thrust to carry a human, gas, and casing? I've seen many videos of small turbojet engines (small enough to hold in your hands) that produce 30-40 pounds of force. If you mounted a couple of these on a small craft, that wouldn't even support human + gas, and especially wouldn't support a fuselage or any other casing.

What size is efficient with gas but still produces a lot more than 40 pounds of thrust?

An extra question you don't need to answer: what is an effective way of tuning fin direction on the exhaust end of one of these engines? Basically, how can I twist a knob and make the fins tighten or twist in a direction I want the thrust to move in?
The figure of merit here is thrust to weight ratio (https://en.m.wikipedia.org/wiki/Thrust-to-weight_ratio)  For a good turbojet, you get about 5:1. So a 100 lb engine could produce about 500 lbf of thrust. Modern High bypass turbofans are significantly more fuel efficient than turbojets, but the thrust to weight ratio is still about 5:1. So calculate how big your human is,  how much gas you want, and divide by 5