Read up on the Detail Tool its purpose is to copy and convert to 2D elements specific areas of the drawings in addition to adding the marker for that specific area. There is no need to copy them to a different file.
If they are Shop Drawings
Your procedure might be the correct one by keeping specific 3D information of the Detailed Assembly without having to coordinate a lot of Layers Etc. This is a good option for general details.
Alternatively you can keep everything in the original project but then you will need to define specific Layers to turn everything off
Which one to use will depend on the project and how far along it is. If the project is changing a lot then go with Layers for all specific assemblies if the project is already past the design stage then separate files are an option.
Eduardo Rolón AIA NCARB AC26 US/INT -> AC08
Macbook Pro M1 Max 64GB ram, OS X 10.XX latest another Moderator
I prefer to keep everything in one file as Eduardo suggested. This means that you will need separate layers to isolate specific items. ie steel columns vs steel beams, wood columns and wood beams. I use a section marker rather than a detail marker to keep everything updated as changes are made. i produce 4 elevations and a 3d view for each item. Not the quickest, but its accurate