Which leads me to the idea that maybe the feature should be better motivated! Perhaps we can show the user a meaningful and well-defined number, comparing for example the sheer size of a normal request vs one made in a container. If necessary, you can dig deeper into the payload, and ask questions of the system like, "What are they saying about me and my activity, using my own browser as a communication channel?" This latter one could be quite fun and take community contributions, small code snippets that know how to parse a request and interpret and display the meaning to the user.
This is where the imagination of a developer can be helpful, to basically characterize as completely as possible the patterns we expect to see. Because so far, that's a very low-level mechanism, and clearly there's more room for protocols - and given the nature of this problem, multiple, overlapping, dynamic protocols that are proprietary in nature. We can imagine origins that just suck everything in, doing unknown processing on that data, but giving us tools to measure aggregate engagement. The need to define an audience on something more than source IP becomes immediately apparent, and permissive 3rd party cookies have enabled a huge ecosystem to arise, and each persistent part of that is specialized in some way. But the money is in showing users ads, and showing them really useful ads. This means measuring the users and trying to anticipate their needs. We can base this on "identity" facts that don't vary much over time, or on "behavior" facts that vary a lot over time, albeit with lots of consistency for most of it. Both are used to predict what a user wants enough to spend money on. In particular, behavior, what are they asking about, learning about? What sorts of tools and supplies - things you can buy - are associated with the subject?
TBH if this happened on the client side, I wouldn't find it creepy at all; I'd find it quite useful. There are really two problems with server side processing of identity and behavior: first, it quickly gets bigoted when people are asked to associate an identity with a consumer demand. Who gets to make this association? Are we okay with this being a self-reenforcing mechanism since we are pushing identities toward the behaviors we associate with their stereo-type? Second, it lets servers split the internet without our knowledge. The incentive to garner as much attention as possible leads inevitably to breaking our shared perception of the world. At least, back in the day, you could argue with someone over a book, and know you have read the same book. But now, the book is a screen, basically a browser, and it is very different for each individual, and no-one is fully aware of this truth.
I'm being utterly serious when I say that these are the kinds of issues, technical and philosophical, that users need to be aware of before they can get excited about a feature like tab containers. Given the level of civic discourse in the wider world, my hope that people would be open to learning about it is slim to none. Heck, even most devs prefer not to think about it, and just make the changes the money wants to make, without regard to the users benefit. Then of course there is the secondary market for this data, law enforcement. You could probably get 80% of a panopticon by just hoovering Google analytics data for "alternative" processing. You get the rest by piggy-backing Cloudflare and the like. The interesting thing about CF and other CDNs is that they can provide an alternate, and unavoidable, surveillance function, since they can use access logs, and you cannot use the software without getting the bytes. This ends up being a strong argument in favor of content-addressable resources, rather than named resources: they would let a client rotate physical access, and these segmented logs would make it hard to recreate a coherent timeline. But not impossible: if enough sources cooperated, the could aggregate their logs and you'd lose your anonymity.
No, what the world needs is not just a defensive thing like tab containers, but a more aggressive thing. Rather than isolate an account's data, why not provide all the connectivity it wants, but poison the well. Manipulate the messages sent out by your computer to mislead these trackers: shift identities, access different resources, do different things in those resources. It should look identical to ordinary host lookup traffic, but the messages will be different, noisy, worse than useless. Maybe call them "active defense containers".