The anger of the Lord burned against ISRAEL, and he incited DAVID against THEM

[TonyChanYT]

Did God use David to punish Israel?

In the ultimate sense, God uses everyone. God used David to punish Israel.

2 Samuel 24:

1 Again the anger of the Lord burned against Israel, and he incited David against them, saying, “Go and take a census of Israel and Judah.”

In this sense, God used David against Israel because David was the head of Israel.

13 So Gad went to David and said to him,
“Shall there come on you three years of famine in your land?
Or three months of fleeing from your enemies while they pursue you?
Or three days of plague in your land? Now then, think it over and decide how I should answer the one who sent me.”

At this point, David had to choose one evil out of 3. God used David to choose the form of punishment.

14 David said to Gad, “I am in deep distress. Let us fall into the hands of the Lord, for his mercy is great; but do not let me fall into human hands.”

David was saying here: Don't let me be the direct object of the punishment. Let all of us be the target of the punishment. So yes, God used David to choose the target and the form of punishment.