In Chrome and Safari, Google search injects analytics via the ping attribute on <a> tags. This sends some additional ping-to and ping-from headers. So Google is still collecting data from who use its search, provided they are not on Firefox. I would assume it does the same for its other products, such as Google Analytics, but I haven't checked.
The "ping" attribute is available to all sites and many content blocking extensions (including ad blockers) block these pings. This isn't changing with Manifest V3: extensions will still be able to block them.
Note that on Firefox and other browsers that do not support "ping", Google Search still tracks which links you click on, but it uses URL rewriting. There are also extensions that block this.
(I work on ads at Google, speaking only for myself)