I don't have a solution for the Ctrl+T issue. I use mainly the default container as with First Party Isolation I don't need to use containers beside some specific use case (multiple accounts), otherwise I put things in containers strictly for the thing like banking.

For the latter I would recommend Simple Tab Groups. It also has a sidebar which I like very much. I understand it may not be the thing you are looking for, but there are a lot of things you will not get anywhere.

https://addons.mozilla.org/en-US/firefox/addon/simple-tab-gr...