Visual Studio versus QtCreator, they just abstract away a lot of the setup magic to get code working. Code is Code and if the setup is correct and works on one you should be able to copy/paste snippets from one to the other and it should work.
Confirm your assumptions that the buttons are wired up for the start and stop sketching functions by putting a qdebug/cout/print statement right at the beginning of it saying you made it there.
Calling sketchEditor->start returns a bool value whether it started successfully or not, print that out.
Why is your work inheriting from MapView? Is that the pattern your professor gave to you or is that how Visual Studio makes new projects?
Welcome to the wide world of debugging, this is what makes or breaks a good software developer.
For reward, if I help fix your problem, then accept it as a solution. I just realized yesterday that this subforum has a widget that shows who has the most accepted solutions for the past month and I am currently doing better than the Esri employees and want to brag about that when I see them at FedGIS next week and at devsummit in a month lol.