I have The Witness on my steam account and have repeatedly attempted to connect it with GOG. I have changed my steam "Profile Status" to Public as instructed but it just can't seem to detect that I have The Witness. Is there something more that must be done for this to work correctly?

Nope. Set to public, save changes, blood sacrifice of a virgin, and there you go. If you did all that, like you said, then I have no idea what could be the problem.

Keep sacrificing virgins until it works.

Not yourself though, that would be counterproductive.

Might be the reason why nothing works on GOG.

Has no one considered how difficult it's going to be to find a virgin?

That explains GOG's shortage of personnel.

Hours later for no reason at all I decided to trace a line in the air with my finger from the sun downwards towards my feet and "coincidentally" GOG connect worked for me. You could say it was due to me just waiting a few hours for somebody's cache somewhere to expire but I'm sure it was the line drawing.