I would think it is option two but in more depth. Therefore I think you should include your methodological approach, if you are interested in particular methods, your theoretical framework etc. I'm not sure what stage you're at but I would structure it along the lines of a research proposal. I wouldn't give a literature review per se but I would include writers or papers that have influenced you, or perhaps on which you are structuring your research design. If it's a competitive process of application (and many summer schools are) you have to demonstrate how much you think what they are offering will benefit you, and what you might contribute to the school. Headings I would include:
Overall topic description
Influencing literature/authors
[proposed] methodology or methodology progress thus far
area you see your PhD contributing to
Good luck
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