How to bid and make a grand slam with 28 HCP between the partnership?
The answer is; you don’t.  Not with normal 2/1 methods, anyway; and even pretty out there methods would have a hard time finding this.
Why?  Because it’s dependent on so many things. The seven card heart fit AND the short jack. The spades splitting 2-2, or guessing the finesse.  The partnership has only eight top tricks, and the rest depend on distribution. In NT even a small slam is risky if you get a club lead!  No one would bid the grand knowing even every card in both hands for EW - you need 70% to bid a grand and you won’t get that here (hearts are 61% and spades are 46% roughly between the length and the finesse possibilities, so the grand is about 30-35%, plus some small chance for a club trick with a squeeze).  6S is probably the ideal bid double dummy (only the spade split is really a problem there, hearts don’t matter, and extra chances appear in clubs).
A normal 2/1 auction is simple here.
1NT - p - 2H - p
2S - p - 4S - pass out
Some would bid 3NT instead of 4S, and some would leave it there.  Some have ways of showing really good spades (superaccept), though KTx feels borderline to me for that. Could the spade hand see the slam?  I guess?  But 28 points and pretty average distribution beyond the one extra spade isn’t super exciting.
Some bidding systems are very control oriented very early on, for what it’s worth, and would find most or all of the eight trucks in the early going plus the space fit.  Things like this precision system would have a shot at the small slam I think.
Don’t assume that the few hands that bid the best score did so by being smarter than everyone else. Usually it’s that they were more risk-taking than usual, or misstated the strength of their hands, and got lucky. But for every top they get for this kind of thing they get four or five bottoms when they’re down 2 in grand slam and everyone else is making 4S+1.