Thanks for the question; FYI we are lay Catholics, not priests.
Last rites are for those who are living. A deceased person has different rites such as the Rite for Christian burial (done at a Funeral Mass).
Even with an assumed suicide, we still entrust the soul of the deceased to God's Mercy. We never know the full circumstances and want to give the benefit of doubt to any given situation, so we let God be The Judge; we should do all we can for the deceased.
In former generations the stigma of assumed suicide sometimes prevented things like having a Christian burial, because the finality of the grave sin seemed to eliminate any chance for repentance.
Today, with a deeper understanding of things like clinical depression we know that the human will is compromised, and a form of mental illness mitigates the freedom of the subject. So in essence, let God, who is able to see everything clearly, make the call.
We are not saying that suicide is not objectively a mortal sin, only that the culpability of the individual is known only to God.