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I'm not entirely sure what all data is sent. But I am doubtful that it would be any kind of critical personal data. Mainly because that would be a massive issue if it did without making the user explicitly aware.
From what i can understand the "parts of site content" refers to things like embedded content or content in general for that matter. For example stuff like text, images, videos that sort of thing in the site which collecting both of those things would likely not process any critical data.
It's also important to note however from what I understand is they will only send the data if they find the site to be suspicious in the first place. Which I don't really see how that could easily happen on a legitimate site.
Your concern and skepticism is quite understandable. Though I think it'll likely be fine.
Also do keep in mind I am not a expert on Google's safe browsing and I may be factually incorrect so take what I say with a grain of salt. I am just saying what I think I understand about it from research on it.
You could also have a peek at some documentation on it and see how you feel for yourself.