Scientific statement for UK application

I am a junior research assistant at an EU based institution. Sadly they don't have enough budget to keep me around so I'm looking for other options.

There's this GREAT supervisor led project at a top UK uni (not Oxbridge tier but definitely a good one). I reached out to the supervisor expressing my interest and he told me my CV looks strong and he would support my application. Which is amazing.

But I'm at a loss on what to do next. Deadline for applying is mid December. I need a scientific statement (max 300 words) that explains how I am planning to contribute to the project and what are the gaps that I am planning to address, without repeating the project proposal itself. I asked the supervisor for a call but he didn't reply, I assume he's very busy. I could maybe ask my current supervisor for help and guidance? I only have vague ideas right now and I'm scared my statement will sound too generic or not focused enough. I started reading the suggested literature but it's soo much information and I feel overwhelmed. My research experience is tangentially related and I don't know if I can manage.