How to add tools to customize tool bar window (pictured below)

I want to see F1-F3 normally so that I can add/ move them around freely by clicking and dragging. How do I do this?

BTT doesn't modify the system Touch Bar. Have a look at some of the existing presets here or the docs:

Thank you. Would you know if there happens to be an existing preset that includes all of the above?

AquaTouch, GoldenChaos are the most famous ones, also very "charged" and might change the displayed actions depending on what modifier keys are triggered.
Feel also free to have a look at my Preset or browse a bit through what you can see in the Preset Section.

I don't really understand what you expect fron the TouchBar Preset, but the easiest solution for you might even be to create your own preset in some easy steps :man_shrugging:t2: Or explain a bit further what functions you are looking for.