Honestly I had the exact same problem with my cat and my humidifier. Tbh I just gave up on the fancy gadgets and moved my humidity loving plants into the bathroom. They get the steam from showers and the cat never goes in there. It's not a perfect fix but it's free and nothing gets knocked over.
Whoa, I'm gonna go the other way on this one. I actually tried a deep pebble tray with a grid and it was a total mess for me. The water still evaporated but left this gross mineral crust all over the pebbles that I had to scrub off, and my cat just pawed at the grid until it flipped over and soaked my floor. Plus I never saw any real difference in my humidity meter readings, so it felt like a lot of work for nothing. You really think that setup held up longer than a day?
Pebble trays never did much for my humidity levels, they just evaporated too fast. I ended up putting a small humidifier on a high shelf behind the plants. The cord is a bit of a trip hazard, but the cat can't reach the mist or the water tank up there.