Container Tabs are completely orthogonal. A site loaded in a tab which is contained in this way cannot access your global cookie jar, for example. If you visit a site with a Facebook Like button on it, then Facebook will not receive the same cookie from you that it would have received if you had loaded the site in a non–contained tab. This is true whether or not the site has been given it’s own process to live in. The converse is also still true; non–contained sites still have access to your global cookie jar even if they’re isolated in their own process.

Putting sites in their own process mitigates against Spectre–like attacks, but it doesn’t do anything for higher–level problems like third–party cookies.

Any idea?

I'd love to drop https://addons.mozilla.org/en-US/firefox/addon/temporary-con..., which automatically assigns a temporary container to any new tab, which plays nicely with the https://addons.mozilla.org/en-US/firefox/addon/multi-account... but uses too much memory (at least from my experience).

Based on the processes I'm now running, it seems that tabs for the same domain but in different containers do (as one might expect) count as separate origins for the purpose of creating one process per origin.

So they do different things, and interaction between the features appears to work without issues.