On the contrary; the browser is still generally the user's agent (although Chrome can be iffy) - we don't need to imagine, because we can compare the Facebook app to browsing Facebook in a browser, and see that the browser is still far more friendly to the user's interests than what FB ships.
It is, although both Chrome and Safari obviously have their own, non-user interests.
But browsers in 2022 are second class citizens, for business models that can generate positive ROI from developer time. They are at best dissuaded (e.g. Reddit, TikTok), and at worse actively crippled or prohibited.
The majority of users are on apps, and more users are moving to devices (e.g. Chromebooks, Portal). All of which are explicitly not user agents.