What you are going to have in regards of SPO integration in teams is the ability to interact with your sites as if you were accessing directly the site in the browser. By the way, this is something you can also get Today with the Web Tab
The new tab coming handles security better etc. but there won’t be a task list option side task lists still are not modernized. I haven’t heard of those being done but they eventually will. Probabaly still 3-6 months out or longer.