As far as I know, it depends on where the click happened.
If the profile showed up in regular Google Search (the local pack or the business panel) and the person clicked through to the website, that click is counted in Search Console like any other Search click, with the query they typed, credited to the page they landed on.
If the click came from Google Maps, it won't show up in Search Console at all, since GSC only covers Google Search. You'd only see it in the Business Profile's own performance numbers: website clicks, and the search terms list, which is grouped and doesn't match up click by click.
To pull GBP traffic out separately, tag the profile's website link with UTM parameters and look at it in GA4. Search Console usually folds the tagged URL into the canonical page, so it won't split it out there.
