I had a low efficiency cat error last year on my 2002 Sienna with 170K or so on it, now it has 183,000. I spent a lot of time Googling, because I am in Mexico, and repairs are hard and expensive. I found there is usually a sensor before the cat converter, and one after.
When the car (ergo cat) is cool, they will read the same, because the elements are not burning the crud. Once they are warmed up, the output sensor should read much lower than the input sensor. If it does not, you get a code for failure. There is no way as such to test the cat, it only compares input with output, and expects a lower output reading.
Obviously, if one or the other sensor reads wrong, it may not show a difference even if there really is a difference.
Most URL’s I found said the problem seems to almost always be the sensors, though of course the cat converters can get clogged up. On my car, it failed after a 17 mile run down the mountains to Orizaba with a one mile drop in altitude, in second gear for engine braking, which means the fuel was turned off. I kept driving it and it went away and has not failed again. My guess is that long a time with the fuel injectors turned off the elements got clogged up from small amounts of oil or something like that.
Most posters here said it will come back, but so far it hasn’t.