Did the Old Testament Jews believe in a triune God?

Not with clarity.

I think we need the category of progressive revelation, which states that stage by stage in redemptive history, greater and greater clarity as to the nature and activity of God comes.

And with that category, no, I don't think that Old Testament Jews were clear about the nature of God in the way that we are clear with the incarnation and the teaching about the Holy Spirit that comes with Jesus.

However, having said that, I want to be careful not to deny that they believed in the triune God. Because they believed in the God of Jesus Christ. They believed in the true, living God as he was being revealed in special redemptive history, and that God was the triune God.

So they believed in the God who is the triune God. And there were hints along the way, such as, "Let us create man in our image" (Genesis 1:26). I know there are various ways to take that text—like as a royal plural or something—but it is still interesting. It's going to be provocative of a plurality in God.

And then the Spirit of God was real. And then there began to be a sense that the Messiah who was to come is no ordinary, mere man. There's more to it than that.

This is why Jesus, I think, made Psalm 110:1 his favorite psalm. He referred to it over and over and over again: "Whose son is the Messiah? And whose Lord is the Messiah?" And he drew out that he was more than a mere man.

So, Yes, they believed in the triune God. But, No, they did not have clarity that he was a triune God. That came progressively and with greatest clarity for us in the New Testament.