Altium Designer: Is it possible to switch layers in an entire library at once?
Three approaches here: we can move every 3D body to Mech 12, or we can move all the Mech 1 objects to Mech 12, or we can move just Mech 1 3D bodies to Mech 12.

Moving all 3D Bodies to Mech 12


Right click on a 3D body in one of the components -> Choose "Find Similar Objects"
"Object Kind" should be "3D Body" with the filter set to "Same." Everything else should be "Any."
Check the "Whole Library" tickbox in the bottom of the Find Similar Objects pane.
The PCBLib inspector will pop open, and all the 3D bodies in your library will be selected. Under the "Object Specific" heading there is a field called "Layer." Open the drop drown next to it and select "Mechanical 12."
You'll get a warning about changing multiple objects and that the action cannot be undone. Click "Yes," and you're finished.


Moving Everything From Mech 1 to Mech 12


Right click on any Mechanical 1 object in one of the components -> Choose "Find Similar Objects"
Change the filter on "Object Kind" to "Any" and the filter on "Layer" to "Same." Everything else should still be "Any."
Check the "Whole Library" tickbox in the bottom of the Find Similar Objects pane.
Perform steps 4 and 5 from the first procedure.


Moving Only 3D Bodies From Mech 1 to Mech 12


Right click on a 3D body currently on Mechanical 1 in one of the components -> Choose "Find Similar Objects"
The "Object Kind" field should be "3D Body." Set the "Object Kind" filter to "Same" and the filter on "Layer" to "Same." Everything else should still be "Any."
Check the "Whole Library" tickbox in the bottom of the Find Similar Objects pane.
Perform steps 4 and 5 from the first procedure.