Not having subdomains work for container assignments is a baffling design decision. It's a well-known issue and oft-requested feature that the devs seemingly have no plan to fix. It's incredibly frustrating.

> whenever I'm browsing in a container tab, I wish CMD-T opened a new container tab

Not exactly what you're looking for, but Temporary Containers (no longer maintained, fwiw) at least will open every new tab in a new temporary container that will be wiped after a configurable amount of time after closing.