I am having a hard time finding the right search terms to locate a very niche type of interior locking door knob.

I have an interior bathroom door that opens against a linen closet door (bad design and not easily fixable with a door stop or hinge stop because of reasons). Sometimes they bump into each other, and the push button lock activates accidentally. We have the pin key hung outside the door, so not a big deal, but a continued pain, especially with young kids running around.

I don't want to switch to a turn-style knob lock, because the raised ridge is going to start to gouge the linen door wood.

I know there exists a type of doorknob that has the lock button on the rose(rosette?) that you can activate with your thumb, but for the life of me I cannot string together the correct search terms to find anything like it online. I went to home depot and lowes to ask around they were both less than helpful.

Does anyone know what this doorknob is called?

And yes I know I could look at trim mounted bolts or privacy latches, but I'd really prefer to find this specific door knob.

Any help is appreciated :)