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A short note is enough.
If you think this may be the right kind of work for you, a short note is enough. You do not need to summarize your life neatly or present yourself in a polished way.
I read inquiries myself and reply as I am able. If an initial conversation seems useful, we can arrange one. If it does not seem like the right fit, I will say so plainly.
It helps to include a few sentences about what brings you here and whether you are looking for a one-off conversation or something ongoing.