You can find these on Amazon as earthquake straps. They work great for bookcases and other things that are close to the wall. If the cat tree has no place on the high end that’s close to the wall you could tether it in the middle.

Are you renting? Are you going to move soon? If not, then, I would not worry too much about how you’re going to cosmetically hide these once you take them down. You will likely want to leave them up for several years, and even more if you decide to have another kid. At some point years from now you will need to remove some anchors and patch some small holes, which is relatively cheap and easy to do. God bless YouTube.

I suggest ANY house do this for heavy furniture that might fall in an earthquake, as well.