You are correct on most accounts, however, I would slightly differ on the view that the PAF abilities should not have been shown. The nature of wars have changed. Previously, the airforce was there to support the Army and the navy and other objectives. But now it is the OTHER way around.
The Air force in the new doctrine is the PIVOT power, and other branches of military will work with it. And that is why you have JF-17 project and also Project AZM.
Also, the the fake surgical strikes drama by India HAD DEEP GEOPOLITICAL AND STRATEGICAL reasons. There are big powers behind it. If on that day, PAF would not have responded and there was no message given to india, the situation for Pakistan would have become very nasty and very uncontrolled on ALL BORDERS very quickly. Now, countries like Iran and A-stan and others know their place, and they have gone back in the little boxes where they belong, and Pakistan is left to deal with India, which they have and continue to do.