If the Holy Spirit is indivisible from the Father in 1 Corinthians 2:11, how can He be a distinct person?

1 Corinthians 2:10-11 says: >"But God has revealed them to us by his Spirit. The Spirit searches all things, even the deep things of God. For who knows a person's thoughts except their own spirit within them? In the same way no one knows the thoughts of God except the Spirit of God." Paul compares the Spirit of God to a person's own spirit — which would imply essential unity, not distinction. In my case, my spirit is not another person; it's just me. If the Spirit of God is likewise indivisible from the Father, as Trinitarian theology also affirms, how can the Spirit still be considered a distinct person from the Father? How do Trinitarian theologians respond to this apparent tension between indivisibility and personal distinction in the Godhead, especially in light of this verse?