amqata

The key here is that inflation falls, not the nominal price level. Thus although the two curve shifts you’ve mentioned do take place and P0 does rise to P2, still on the LRAS, it’s less than the hypothetical mentioned above where “aggregate demand increases (shifts to the right) by an amount that is less than originally expected by the market”.
Had the policy not been implemented, AD would have risen further and inflation would further have increased. Were the policy implemented but not credible, the government would have had to pull inflation down slowly by lowering inflationary expectations  causing a recession and thus moving to the right on the Philips curve (higher unemployment, lower imflation).
A bit hard to explain without graphs!