Inverters can give off conducted and radiated EMI, sometimes that interferes with electronics and radios. Radiated drops off as r^2, while conducted is confined to the wire and won't drop off significantly
There are also near-field magnetic fields, especially from transformers. That drops off as r^3.
My wife got an E/M field meter, and sure enough, microwave gives off a strong field. That is from the transformer, of course, not the microwave tube. She now keeps the cats away from it when operating (unlike your cat, ours don't seem to instinctively realize it is depleting some of their nine lives.
In a similar vein, my wife became concerned about the Covid shot and was quite unhappy that I got it. She saw demonstrations in videos that it causes people to become magnetic, apparently because it contains only graphene nanoparticles. I have some super magnets from Harbor Freight, so I put on on my arm where I had been vaccinated. It stuck. I tilted my arm until the magnet was on the underside and it continued to stick. I then transferred the magnet to my right arm which hadn't received a shot yet, and the magnet slid right off.
I am working on reduction of magnetic fields at work especially from power transformers. One of my colleagues does this by wrapping copper and mu-metal around the outside. The copper serves as a shorted turn, cancelling leakage fields (it does not pass through the core like the windings. Mu-metal blocks magnetic field. With relatively thin material we get an order of magnitude reduction. My effort is is in the area of locating secondaries to better cancel leakage field of primary, and altering phase of multiple transformers to provide better cancellation at a point in space where we have sensitive equipment.
You may be able to apply a couple of those techniques to your problem - add copper and mu-metal bands around the inverter's transformer. You may also be able to make a couple coils wired in series with the transformer and positioned around it - tuned to the optimal number of turns it could provide cancellation. I would use a Variac and resistor to adjust current in a coil, the recalculate number of turns needed.
But to see if the inverter is the issue at all, you could try A/B tests substituting a remote power source, also try relocating the inverter elsewhere. Besides the EMF you think is the problem, there could be inaudible sounds the body reacts to, and there could be flickering of lights.
emf-protection.co.uk
I am not trained in electronics at all
masterpeacebyhcs.com
