Copying folders

I’m new to googology and wanted to see if I can create a big number without writing any exponent towers or Knuth’s up-arrows.

On the desktop of a computer, there is a top folder. It contains two sub-folders which contain two files each.

There is also a button.

When you click the button, all currently existing files will perform these steps, one after another:

- Copy the top folder, then simultaneously paste it into all other folders (at all depths)

Any time a file is created:

- Create a new button and place it right on top of all other buttons, perfectly overlapping (any clicks on the button will click all stacked buttons in succession)

f(10) means clicking the button 10 times. The big number is the total number of folders in the folder structure.

I guess it’s big… but how big is it? 🧐