Maybe? I’m definitely not an expert in inductive charging. I would think a cat laying between the charging pad and the receiver would be getting a big hit of radio waves. Maybe not.
If you put a chicken breast in a microwave oven and turn it on, it will rapidly cook. If you stand next to a radio antenna emitting hundreds of watts you can potentially get burns. These things use electromagnetic radio fields (E + H) to blast energy out, and those fields can stably radiate out on their own.
Inductive cooking and charging is radically different. If you put a chicken breast directly on an induction cooktop and turn the cooktop on, nothing happens. The unit doesn't even really increase its energy usage, because there is no load. This is because this energy transfer is relying on just the magnetic fields (H). It relies a lot on the target being harmonically in tune, and the other side needs to actually be conductive and at least somewhat magnetic. Non-magnetic materials don't couple with these magnetic fields. This is why some pans (like aluminum and copper) "don't work" with induction cooktops.
So if a cat did climb on the charging pad, maybe some parts of the collar would energize and heat up.
If animals were significantly affected by things like wireless charging pads or inductive cooktops we wouldn't be able to survive MRIs.
Regardless, your MRI comparison is very apt. MRIs use similar amounts of energy for scanning and do sometimes cause burns. But no one seems to be getting cooked.
> that the transfer is via electromagnetic waves.
An induction charger doesn't transmit its energy through electromagnetic waves. That's what I'm saying. It's inducing a current through magnetic fields. Its a very different process. If the material isn't magnetic it doesn't react. Which is why a steel pan heats up very rapidly while your hand is cool, why an induction stove doesn't use much electricity at all when there isn't a pan on it to heat. If it worked by emitting RF, it would have the same power output regardless of the pan type. Which is like your microwave, if the magnetron is energized it's putting out 1,000W regardless of what you have in there.
A radio is emitting its power regardless of if there's an antenna on the other side tuned to receive it. If there's nothing on the other side of the inductive charger, there's no load, there's no power usage. You need something able to receive the power to actually transmit the power. With that something being how well it reacts to magnetic fields.
So while I buy the distinction between magnetic coupling and propagating EM waves, it seems that there is some risk.
Maybe at 11kW+ of effective power delivery these fields are enough to actually make eddy currents in your blood enough to cause damage. There's a decent chance it could cause neurological disruptions while in the field. But once again, its really not the same kind of thing as RF radiation emissions, and how these things will affect you is pretty different in the end.