The pivot
Hal announces the strategy change in his second scene on stage, alone, before anyone has asked him for one. He executes it two plays later. The interesting part is not the pivot. It is that he tells the audience the plan and tells nobody in it.
He has been drinking with thieves for one scene. They leave. He turns to the house and explains what he is doing.
I know you all. Not I have fallen in with these people. He has assessed them, priced them, and scheduled their usefulness. The tavern is a positioning exercise, and the low expectations he is building are the asset. He says so in the same speech.
My reformation glittering over my fault. He is not planning to become better. He is planning to be seen becoming better, and he has worked out that the size of the reveal depends on how bad the before picture is. The disappointing years are the investment. Read as a business document it is a competent one, and it is stated in the first act so nobody can accuse him later of improvising.
The day it lands
Falstaff hears that Hal is king and does not wait to be summoned. He wakes Shallow in the middle of the night, starts promising him an office, and says out loud that the laws of England are now at his command. He rides to the coronation to collect. He gets to the front of the crowd and calls out to the new king by the name he has always used.
I know thee not, old man, against I know you all. The same verb, four plays apart, and the second one is a lie that everyone present can see is a lie. That is the point. The public denial is the announcement. Falstaff is not being punished for anything he did that week. He is being used one last time, as the visible cost of the new direction, in front of the largest audience the new king will ever have.
Note what Henry does not say. He does not say the old strategy was wrong, or that he was young, or that circumstances changed. He says he has turned away his former self, which puts the change inside him and outside anyone's ability to argue with it.
What the pivot actually costs
The plan works. Henry becomes the king the next play needs him to be, and the country gets a competent monarch out of it. Judged on outcomes it is hard to fault.
What it costs is legible only to the people who were in the old plan. They were never told there was a plan. They were told, by omission and by four years of behavior, that this was the arrangement. When the pivot came they found out the same way the crowd did, and the fact that Hal had been transparent with the audience since Act One does nothing for them, because they were never the audience.
Anyone who has announced a change of direction has a version of this scene available to them. You can run the pivot without the coronation. Henry chose the coronation because the denial was worth more to him in public than the man was worth to him in private, and Shakespeare gives you both the soliloquy and the rejection so you can price that trade yourself.