Question 2 is worth testing on day one of any trial, because it is where the thin wrappers fail and it is trivially checkable.
Start a session in the wrapper. Close the wrapper. Open your normal terminal and try to resume that session. If the agent's own resume finds it, the wrapper is a view onto real state and you have lost nothing. If the session only exists inside the wrapper, you have taken on a dependency for every session you start in it.
That second kind is not disqualifying — plenty of good tools own their state — but it converts "I could stop using this tomorrow" into "I would lose my history", and you should know which one you agreed to.