but here’s some proof that I’m competent enough to join you if you need me, so please don’t kick me out?”

Most of the ones that do this, sit proudly as if expecting something in return, to show “Ok whisker, you’re indeed competent.”

can you show me how to do the make it delicious part like you do to your kills?

Those tell you, even jump on the kitchen to see how it’s done. Some even go as far as imitate things they saw when you cooked last.