No, none of those say spiritual baptism. You invented that.
Baptism with water was foreshadowed in the OT both in the story of Noah and the flood (see 1Pet3) and in Number 8: 6-8 & 21
“Take the Levites from among the Israelites and cleanse them. Thus you shall do to them, to cleanse them: sprinkle the water of purification on them, have them shave their whole body with a razor and wash their clothes, and so cleanse themselves……The Levites purified themselves from sin and washed their clothes”
After his speech at Pentecost, Peter said to those assembled: Repent and be baptised, every one of you, in the name of Jesus Christ for the forgiveness of your sins. (Acts 2:38)
Ananias to Paul: Now, why delay? Get up and have yourself baptised and your sins washed away, calling upon his name. (Acts 22:16).
Washed away is apolouo. The only other time this appears in the Bible is 1Cor 6:11
but now you have had yourselves washed, you were sanctified, you were justified in the name of the Lord Jesus Christ and in the Spirit of our God.
Then in Col 2:11-13 Paul says
In him also you were circumcised with a circumcision made without hands, by putting off the body of flesh in the circumcision of Christ; and you were buried with him in baptism, in which you were also raised with him through faith in the working of God, who raised him from the dead. And you, who were dead in trespasses and the uncircumcision of your flesh, God made alive together with him, having forgiven us all our trespasses,
The point is that it is baptism (with water) that God forgives out sins and brings us the new life in Christ.
This renewal was also foreshadowed in the OT
So Naaman went down and plunged into the Jordan seven times at the word of the man of God. His flesh became again like the flesh of a little child, and he was clean. (2Kg 5:14)
And in the NT
“..he saved us, not because of any works of righteousness that we had done, but according to his mercy, by the washing of regeneration and renewal in the Holy Spirit.” (Titus 3:5)
Yes, spiritual things happen in baptism. But that doesn't mean the baptism is spiritual.
OK, Mungo! You just keep trusting in that person who made your salvation possible when they performed a water baptism ceremony on your behalf. You can explain all of it to God when you meet Him, no need to explain it to me.