How to proceed with a postdoc research idea?



I am a UK-based PhD candidate with viva scheduled in a few weeks' time. I have a research idea that I would like to work on post-graduation, and I have also identified an organisation (in the UK) and a potential PI, whom I'd like to propose my project to. However, being a first-gen academic, I don't know how to go about these things, and I don't really have anyone I could ask for advice on this matter. So, what would be the 'correct' way to start moving things forward, considering that I don't currently have any funding or affiliations; should I approach the potential PI directly to enquire whether they would be interested in the project/hosting me/collaborating in funding applications, or should I try to secure funding first? Also, if approaching directly, should I present a full research proposal at the first contact or, initially, just a short email with a brief summary of my idea? Do I need to be worried about being 'scooped' in case they were not interested in collaboration?

Any advice would be greatly appreciated!