Is failure to fully adhere to the zakat threshold, after a previous supplication to allocate a portion of one's provision to the poor, considered hypocrisy for which one will be punished by Allah, just as happened to those mentioned in Surat At-Tawbah, whose charities were rejected and whose repentance was not accepted?

Breaking a promise is a sin, and it can lead to hypocrisy in the heart, but it does not negate the acceptance of repentance. Sincere repentance is accepted even from disbelief, and it includes hypocrites who broke their promises. The story that claims the Companion Tha'labah broke his promise and his repentance was not accepted is false. A Muslim must repent when committing a sin and not despair of Allah's mercy.

Your supplication, "Our Lord, grant me provision and give to the poor," is a vow of obedience that must be fulfilled, and you have done so. As for your shortcomings in Zakat (definition), you have begun to rectify them. Do not pay attention to whispers and continue with your worship.