Chemical engineering super curricular activities suggestions.

I am nearing the end of year 12 and I have don’t a ton of extra curricular activities such as volunteering and maths tutoring.
I also will be doing a Mark Everson project with my friends soon too.

However I don’t really have anything for specifically what I want to do at university, chemical Engineering I have applied to Eton and Nuffield program but was unfortunately rejected.

I plan on attending astronomy club after the Half term and I also have a confirmed place for work experience at a local pharmacy. I also attended a maths competition at the start of the year

What else should I do over the summer in order to have a suitable and competitive personal statement for university?

Focus on your grades. Astronomy and pharmacy aren't relevant to chemical engineering (though astronomy certainly can be interesting in of itself). A maths competition is slightly more relevant as maths is a key subject for engineering, but what will be much more relevant is your actual grade in A-level or equivalent in maths. And chemistry. And physics if you do that.