The public declaration made by the Israelites serves as an absolute confirmation of Samuel's flawless integrity throughout his years of leadership. The people's response is not random; it precisely mirrors the specific questions the prophet had just posed to them. When they confirm that he never cheated them, it directly answers his question about whom he might have cheated. Their statement that he never oppressed them responds to his inquiry about oppression, and their declaration that he took nothing from anyone corresponds to his question about whose property he might have taken [אברבנאל].
The people structure their response by moving from lighter to heavier offenses. By first denying relatively minor wrongdoings, it becomes obvious that Samuel never committed actual, outright theft. Going even further, they testify that he did not accept a single thing from them. This includes gifts or items he was fully permitted to request by virtue of his official position, as he refused to derive any personal benefit from another person [מלבי״ם, צאינה וראינה]. They emphasize this to make it completely clear that he took absolutely nothing at all [מצודת דוד, ביאור שטיינזלץ].
Even though the entire nation unanimously testifies to Samuel's honesty, human witness can only confirm a person's visible actions. Since no person can know what happens in another's heart, a divine testimony becomes necessary later in the gathering. God's validation confirms that Samuel never even entertained the thought or desire to accept a bribe. This heavenly proof of his pure, hidden intentions is meant to show the people that the presence of God dwells among them, examining their innermost thoughts. Ultimately, this divine involvement demonstrates to the Israelites just how unnecessary it was for them to demand a human king [אהבת יהונתן].