I'm not an Engineer (in the modern sense, whatever that is), but I am the son of an engineer and considered becoming one.
"There's a stereotype that engineers do things by themselves"
Dang right. That's how non-easy problems get solved. Most 'engineering" problems have almost too many conflicting variables and approaches for one brain; way too many to share between brains. Smart minds can balance approaches faster than they can talk about them. Keep the core brain-work in one brain. See "Mythical Man-Month": adding more brains -slows- the process. Interbrain communication and coordination exceeds actual thinking.
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passing accurate documentation to support groups in the right format and in time
Right. It's like cutting a chicken. Most big problems can be cut into smaller pieces at "easy points". Legs, wings, neck. Sometimes you use a big cleaver: split breast, so you have two equal problems. Then you can fork each sub-problem to a different brain. BUT each brain must know the scope of its piece (whole leg or just drumstick?) and how it was/will-be connected to the other pieces. If we re-assemble the chicken, is Torso responsible for supplying blood to Legs, or must Legs do their own blood supply? Will the editor subroutine pass text to the spell-chucker, or must the spill-checker pull text from a shared buffer? In a God-crafted creature, those decisions are already solved; city sewers, word-processors, and other man-bodged projects don't always have clear guidance.
The old book "Code Complete" has many examples of software projects, cut-up and joined at interfaces, where both teams or neither team solved some key problem, and this was not noticed until final assembly. Minor examples abound in all software. What is the EXACT interface? What is expected, what will be supplied? Do car-doors ship in crates? 5/4" #2 oak crates?? (Henry Ford got bids for Model T body-stampings. The final contract specified very special crates. He manipulated the assumed purchasing interface so he got free floor-boards with his stampings. More often interfaces are so sloppy that everybody loses.)
Much of the best engineering is one-man(/woman) work, albeit interfaced with everything which came before and all that can be butchered-off or bought-in. WordStar 2 was one guy in an attic, with the Z80 CPU manual (decent interface documentation). Stevenson's steam engine was mostly Stevenson, but standing on the shoulders of Newcomen and Watt and other steamheads, and ordering-around skilled machinists and foundrymen (prior-art and craft interfaces). Roebling and his son built big and small bridges with one main brain directing many hands and helper-brains. The industrial steel buildings which fell down were drawn by one team and signed by a Professional Engineer, interfaced with little more than a $50 check. The full design factors were not really interfaced to the PE, and for $50 (he was sick and needed the money) he didn't care. This interface was so weak, that when the fallen-down buildings went to court, even though a PE is supposed to be legally liable, the judge released the PE from the suit.
My father the EE did, late in career, wish he'd developed communication skills. He knew what was in his brain, but imparting it to others was tough, often futile. Good technical writing is a special skill. I tried to get a degree in that but realized that my professors were addle-brains, couldn't write-up how to tear your way out of a paper bag.