Just because Jesus' task of bringing salvation to the world through his death, I don't assume that He is no longer involved in the world. "For by Him all things were created, both in the heavens and on earth, visible and invisible, whether thrones or dominions or rulers or authorities -- all things have been created through Him and for Him. He is before all things, and in Him all things hold together" (Colossians 1:16-17). In the same way, I don't assume that God the Holy Spirit had only one task.
We know that the Holy Spirit was heavily involved in bringing the Bible to us (see The Holy Spirit's Work). However, I don't know all that the Holy Spirit is involved in. As God, I would expect His activities are beyond my comprehension. "Oh, the depth of the riches both of the wisdom and knowledge of God! How unsearchable are His judgments and unfathomable His ways!" (Romans 11:33). But I do know that the Spirit intercedes in our prayers (see Does the Holy Spirit only work through the Word?). Just because the Bible doesn't list all of God's activities, I don't conclude there is nothing else for Him to do.