I deal with this all the time and am also normally just interested in the polylines data.
Also, I get CAD files from numerous sources so the format/layers/etc. is never the same.
I have a separate project set up in Pro connected to a bunch of output layers in a FGDB. In Pro, I use the feature class to feature class GP tool, and for the input, I navigate to the Polyline data 'inside' the dwg files.
Since there is no consistency from designers, I use CAD or Pro (think you can use TrueView also) to find out what "Layer(s)" in the dwg holds the lines that I am interested in and set a Where clause in the fc2fc tool to Layer includes the value(s), and pick all the layers that hold the desired data.
I run this tool for the data I'm interested in (sewer, water, storm lines), then close that project.
I then open my AsBuilt editing project that is already connected to the layers I output above.
It's been a while since I tried the GP tool that @Eugene_Adkins suggested as I was only interested in a small subset of the lines from the dwg. Might have to take another look at that, but thought I'd chime in about one method that has been working well for me.
R_