Since WordPress 3.5, the old media manager filter (media_upload_tabs) is still working, however the UI has moved away from the ThickBox used before.
I haven’t been able to find any information that suggests a new approach to add tabs and I wonder if WordPress is going to stick to the old way of adding tabs, or switch to the new way in future.
Does anyone have any insight into the best way to add tabs to the Media Manager?
Unfortunately it’s very difficult to predict whether or not someone will make changes in WordPress, as an Open Source project you yourself could make that decision, contribute code and have the outcome you desire to some extent.
Fundamentally however the old adage ‘if it ain’t broke, don’t fix it’ applies here.
It is hard to know from your question exactly what you are trying to do but there is a lot of criticism by the community as the Media Manager is now very dependent on jQuery and JavaScript and so you may have trouble implementing your functionality in the old way.