The change of phase matters
Under IFAB Law 10, match warnings and cautions do not carry into the penalty shoot-out. A player sent off during the match remains excluded. Those are different disciplinary states, even though a broadcast may show both with card icons.
Consider a defender cautioned during the second half who remains on the field until the draw is decided on penalties. If that player later receives a caution during the shoot-out, adding the two television icons together as if the same phase continued gives the wrong explanation.
Make two short records
Keep one note for events during play and another for the shoot-out. In the invented case, the first note contains the second-half caution; the second begins with the later shoot-out incident. This is more useful than a running total of all yellow images shown during the programme.
The distinction also explains why a commentator may mention a previous caution without predicting an immediate red card. Mentioning history does not mean that history carries into the new ledger. Conversely, the phase change does not let a previously sent-off player rejoin the eligible group. Look for whether the earlier decision was a caution or an actual dismissal before interpreting the later shot of the player.
Questions answered
Does a shoot-out erase a red card from the match?
No. A player already sent off cannot take part.
Should I add every yellow icon across both phases?
Use separate match and shoot-out caution records.
Sources & further reading
Official references for the subjects discussed. Service terms and device software can change.