Is there any evidence Mozilla has plans to do this? As far as I know, there's only two companies doing what you describe: Microsoft and Meta. Microsoft being the most invasive (and evil) by a huge amount—because it's at the OS level.
Microsoft is definitely the most overt in all of this, but Google is working on built in WebAPIs[1], Opera has integrations (sidebars too), Brace includes Leo, and then of course there are the "AI first" companies like Perplexity, Arc etc...
The problem is often that almost all browser features lurk in the background without you really knowing whether they are active or what their scope really ends up being. Cookies, javascript, and various other aspects of the reality of using the web have been abused for mass tracking (and surveillance)
So what's this got to do with Mozilla? Unless Mozilla is encouraging the use of local models, they are just encouraging the development of the same technology that has gotten us into this trouble in the first place. Maybe they should continue the work that meta started -- support development/use of open models of AI and guarantee the AI feature will be completely sandboxed in useful ways.
I also don't need / don't want it's manipulative presence around.
Not to be paranoid, but it's not just about browsers, that's just the most convenient place we've gotten started with this sort of mass surveillance (and control) architecture.