I like your post. It does conflate Privacy Sandbox with one of the specific proposals, however: "there still exists an algorithm which is fed a user’s browsing history and that algorithm is used to put the user into an advertising cohort. However the interesting change with Privacy Sandbox is that this algorithm is run locally within the user’s browser, and never actually needs to transmit the user’s browsing history over the internet. Instead only a code for the identified cohort is transmitted, and a remote ad server can use that cohort directly." is describing https://github.com/WICG/floc

Another component of Privacy Sandbox is Turtledove (https://github.com/WICG/turtledove), where advertisers can tag a user as belonging to a "interest group" and then later on can target ads against that interest group. Which groups a user is in is maintained entirely by the browser, and never sent to the server, And any ads that are rendered based on interest group targeting have to execute in a special "fenced frame" which prevents them from leaking information to the surrounding page or to the advertiser in a non-aggregated way.

(Disclosure: I work on ads at Google, so I'm following these proposals. Speaking only for myself)