Here you can see five candidates for the VTOL engine. I have no idea if any of the candidates is viable. In the sketches black means static structure and red means rotating component. Green means a bearing and yellow a seal. Blue arrow means cool air and red arrow hot exhaust. Dotted lines means that the structure has holes. All designs have air intake from below of the compressor. The candidates has no central shaft, the compressor and the turbine are connected to same rotatig component. My estimate for the thrust-to-weight is more than 50:1.

First candidate has only one bearingpoint. This could work if the rotor would be stiff enough.

Second candidate has another bearingpoint. This makes the structure more robust also more complex. This means more weight.

Third candidate has rotating exhaust exit with rocket engine design. Propably makes no sense.

Fourth candidate has a cylinder shape burner.

Fifth candidate has a rocket shape burner and there is no nozzle.

These kind of jet engines shouldn't be used in a consumer market because of the pollution. Small commercial jet planes or emergency aircrafts would be perfect targets. I am quite sure that the generals would use them in military aircrafts too.