Your description claims that Google sends topics to site X only from history related to site X.
Which makes this useless from advertising point of view. Which also means that Google is using the whole history to come up with "rough tooics".
Let's see:
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With Topics, your browser determines a handful of topics, like “Fitness” or “Travel & Transportation,” that represent your top interests for that week based on your browsing history.
https://blog.google/products/chrome/get-know-new-topics-api-...
The browser observes and records topics that appear to be of interest to the user, based on their browsing activity.
https://developer.chrome.com/blog/new-in-chrome-115/
With the Topics API, the browser observes and records topics that appear to be of interest to the user, based on their browsing activity. This information is recorded on the user's device.
https://developer.chrome.com/docs/privacy-sandbox/topics/ove...
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