If you are shown a product ad whilst browsing searchengine.example and then later look up the product at reviews.example, then end up making a purchase at shop.example, your Mozilla browser will send all of these events to one or more aggregation services that allows shop.example to understand (at least in aggregate, assuming you trust the cartels running the aggregation services) that you were exposed to their product at searchengine.example and further exposed to their product at reviews.example.
Where previously an ad tech company was ultimately able to track users based on source IP address (even if cookies had been disabled by a user), IPA now allows these companies to track users across multiple IP addresses, and regardless of the user's cookie settings, via a unique tracking identifier. It is also proposed that the operating system provides the unique tracking identifier which can then be used by all applications or browsers on a device, allowing different devices behind a single IP address to be distinguished.
Most of these private attribution systems are specifically designed so that the people running the ad can count how many people clicked their ads, but not who clicked them or what other things they did. Safari had a proposal in which you could only have a certain number of campaigns running per domain, so you couldn't set up a separate """campaign""" for each user and fingerprint them all at once. I don't know how the Mozilla proposal differs.
Whether or not user-agents should care about this sort of thing is an orthogonal question.
[0] https://www.theregister.com/2023/06/29/google_trueview_skept...
[1] Remarketing in particular is responsible for the "feeling of being seen" from modern ads where you search for one thing and get 10,000 ads for the thing for the next week
User Agent. Not advertiser agent, not government agent. USER AGENT!