Starting from the old syntax, you should have written
connect(ui->SettingsButton, SIGNAL(customContextMenuRequested(const QPoint&)), this, SLOT(ShowContextMenu(const QPoint&)));
Because ShowContextMenu is a member function of QtLauncher. Somewhere in the output (when running the application) you should have seen that this connect didn't work.
With the new syntax this becomes
connect(ui->SettingsButton, &QToolButton::customContextMenuRequested, this, &QtLauncher::ShowContextMenu);
If you try to put in ui->SettingsButton instead of this, the compiler will complain immediately. By writing it out, hopefully you see that the slot is from the class QtLauncher and thus needs an object of this types.
Unless you have other changes in your code, your current solution should not work. You showed that ShowContextMenu expects a QPoint. However, you are now handing it a QToolButton. Try to connect directly if lambdas are not totally necessary.