Why does it look like "instead of us" to you? That is what you need to explore.
BUT more to the issue, just because it looks like "instead of us" to you does not mean it means "instead of us". Lean not on your understanding.
The passage itself (the text, "what is written", God's actual words) does not state "instead of us", nor does it necessitate that meaning.
I believe the words teach exactly what they state. How, you may ask. Because I believe Scripture interprets Scripture.
The OT sacrifice system does not present the sacrifice as being killed instead of the people but as a provision for the priest to make atonement for their sins. The animal needed to die so the people would not, but the animal was not sacrificed "instead of the people". The priest made atonement by taking the blood and applying it in the Most Holy Place.
We also have Christ as a representative substitute (Son of Man, Secondly Adam). This is not "instead of" but "on behalf of".
We have the passover. The lamb certainly had to be killed for the firstborn sons of Israel to escape death. BUT the lamb was not killed "instead of" those people.
Then we have God setting forth Christ as a propitiation through His blood to be accepted by faith. This is not "instead of" (obiously).
I think you are mistaken about the Passover lamb. The firstborn would certainly have died had the Passover lamb not slain instead of them and the blood applied to the doorpost.
It is a life laid down by Christ to redeem life. It is life for life. The source of eternal life for the gift of eternal life. I’m not sure why you don’t see that. But do you think that means there is a need for some to have their sins paid for by themselves? Certainly any may apply the blood of the perfect Passover Lamb to themselves. Jesus died once for all not once for some. So atonement having been accomplished…
Romans 4:7-8
Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered.
Blessed is the man to whom the Lord will not impute sin.
Because the blood of Christ has been applied to them. Sins covered by the blood, righteousness imputed as it says in verse 6..,
(Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,)
And sin
not imputed!!
Why should sin need to be imputed??
Because it has already been paid for, but the Saviour rejected.
John 3:18
He that believeth on him is not condemned: but
he that believeth not is condemned already,
because he hath not believed in the name of the only begotten Son of God.