I don’t think sectoral shifts are the main story (it’s weak AD much worsened by slow TFP and indeed partly caused by longer-term weak TFP), but I view them as underestimated nonetheless. This Karl Smith post looks for them and comes up with only a bit. He does find this:
In terms of employment the main restructuring has been from government to manufacturing.
I don’t think that standard classifications (Mining and Logging, Financial Services, etc.) are always the best way to look for sectoral shifts. I am struck by this paper (does anyone know of an ungated copy?), by Claessens, Tong, and Wei, which looks for sectoral shifts across credit-intensive firms, trade-intensive firms, and I would add to that firms which sell goods to the damaged segments of the middle class. It’s still not going to make sectoral shifts the main story, but it does make sectoral shifts a more important part of the transmission channels. It also shows how tightly connected are sectoral shifts and the AD shocks.
This paper also indicates that monetary policy is more effective than fiscal policy in the recent downturn, in particular for reversing some of the negative shocks to credit-intensive firms.
Addendum: Here is a relevant paper from Chris Reicher.