The deaths depicted on your (misleading) Israel chart resulted from the corresponding rise in Delta cases over a month prior. That surge in cases, and the prevalence of “breakthrough” infections among the vaccinated is what prompted them to begin giving boosters to the vulnerable.
The chart also cherry-picks a cutoff date, just exactly before deaths plateaued for two weeks and then began its ongoing decline - as booster rollout gained speed.
As published in the Peer reviewed New England Journal of Medicine on 7 October 2021, this is the real effect of boosters in Israel:
“ At least 12 days after the booster dose, the rate of confirmed infection was lower in the booster group than in the nonbooster group by a factor of 11.3 (95% confidence interval [CI], 10.4 to 12.3); the rate of severe illness was lower by a factor of 19.5 (95% CI, 12.9 to 29.5).”
