The second person of the Trinity is the Word.
At the incarnation the Word took on flesh and became Jesus Christ.
His flesh is 100% human. But it did not exist until the incarnation.
His spirit is the second person of the Trinity.
Just like we are a union of flesh and spirit without them ever becoming one substance, so was it Jesus Christ.
When they refer to the eternal existence of Jesus in the Old Testament it concerned his spirit, not his flesh.
When they talk about Jesus as Messiah it concerns his flesh.
His flesh died on the cross, his spirit did not.