The HF is somewhat isolated from the existing SCR switches in the inverter by the reactor, which also smoothes out the nasty switching transients from the SCRs - while they are off the freewheeling diode and the reactor inductance keeps the arc current going (but decaying, to be boosted when the SCRs are on, thus the AC ripple on the output). So before the reactor you see SCR switching transients, and after it you see HF starting noise (if it is on, so don't turn it on) and arc noise (unavoidable).
The electromagnetic fields from all those high currents being switched will couple into every piece of wire in the general vicinity, regardless of which side of the reactor you are on, unless you take precautions to prevent it, like using shielded boxes with all I/O differential with good common mode rejection. Books have been written on the subject.