Dear Anathama Sit,
The priest’s absolution in the Sacrament of Penance is complete, for all sins confessed and those forgotten.
The “minor” absolution at end of the penitential Rite at the beginning of Mass, or beginning of a communion service, or communion to the sick does NOT have the same effect as in the specific Sacrament of Penance. That is why I call it “minor” in quotes. Also, to confirm that it is not the same, the celebrant who speaks the “minor” absolution to restricted from making the sign of the cross over the assembly at this point. This used to be done, but became an abuse when various priests claimed this was an act of GENERAL absolution. People stopped going to the Sacrament of Penance (and that has hardly recoved from this blow)…they thought, “if I have received General Absolution, why do I need to go to The Sacrament for forgiveness.”
Also, in a community penance service, the actual recounting of sins and absolution must be done individually (personally), to/by a priest. It would be very unusual (emergency, battlefield) for a priest to give GENERAL absolution. That is prohibited under “normal” circumstances.
IMHO, the act of penance and contrition at the beginning of the noted forms of Eucharistic Liturgy is not there by accident, any more than it was in the Tridentine Mass (EF). I think it was placed there, in that way, for contrition for venial sins (faults). That is personal opinion.
Peace be with you.