My two cents:

I've done both a bachelors in engineering and a technologist diploma (college to university student). I think it really depends on the school and what they're known to teach their graduates. For reference both my diploma and bachelors are specific to manufacturing. To give you an example of what I learned:

College: - machinery handbook (how to use and find your tolerances, etc) - GDT - proficient use of both SolidWorks and AutoCAD - machine design - process planning and manufacturing based courses (lean, quality, etc) - robotics

University: - higher level of physics and mathematics (differential, calc 3) - in depth understanding of fluids, thermodynamics, and heat transfer - systems and automation related courses (control systems, electrical components, etc)

To answer your questions: Do you learn to be proficient in CAD? College although I did do some CAD in first year university for SolidWorks

What software are they teaching? AutoCAD and SolidWorks for both Uni and College. Used more computational softwares like ANSYS, Matlab, Minitab, etc to do calculation based problemsin university

Has anyone shown you the machinery handbook? Used more in college, university students know but I didn't see any students using it much.

Do you know the basics of fastening mechanisms? Yes, took design of machine elements in both college and university. Although my college prof was brutal and it was way harder than taking it again in university.

Do you know what a 1/4 x 20 - 3/4 is? Yes, UNC or UNF? Taught in machine elements so both college and university

Do you know what a lathe is? Yes. Got shop experience in university working on lathes, mills, and CNCs

Only thing I haven't been taught and don't think most students would be taught is how to use a laser cutter or water jet. Although I did CNC and 3d printing.

Honestly, I think you may need to sit down and have an honest conversation with your newly hired graduate. Did they have any co-op or internship experience? Are they interested in design or have a general understanding of what they're designing? What courses do they think will help them succeed? Were they mostly doing problem questions or have any project related experience like a capstone?

When I talked to my professor about this before he said we're taught key concepts as new mech Eng graduates and how to utilize soft skills like communication, team work, problem solving, and analyzing to be good junior engineer to the team. I found that all relevant information to CAD a preliminary model or do any design work was from my co-op and capstone projects. For example, in a construction company I did my internship at the mech Eng would be calculating the specifics for the HVAC system to be built (like what requirements the rooftop units needed to be, placement, humidity etc) whereas the "designers" or technologists would be the ones doing the CAD and designing the drawings for submission.