To be honest, they didn’t help me out at all. The sent me instructions how to customise the switcher itself within the Squarespace platform. If they had taken a look at my website, they instantly would have seen that I know how to do that, I even used CSS to tweak it even more. I didn’t ask for help on that.
For placing the switcher on my mobile header instead of in the overlay menu, my question, they said: well, that’s up to squarespace (basically).
So my question still remains unsolved 😉