I have read the Baptism by Blood(being killed as a martyr) is a “second baptism”, with the same effects as water baptism(washing away all sins and temporal sins, no purgatory).
I think it is a “second form of Baptism” not a second (repeat) Baptism. Same as Baptism by fire (internal desire). Baptism does wash away sins.
The Catechism of the Catholic Church states
“The Church has always held the firm conviction that those who suffer death for the sake of the faith without having received Baptism are baptized by their death for and with Christ. This Baptism of blood, like the desire for Baptism, brings about the fruits of Baptism without being a sacrament.” CCC1258
Keep in mind that a person can only be Baptized once because the Sacrament of Baptism leaves an indelible mark on the soul which can neither be removed or repeated.
Also, keep in mind that suffering with the correct disposition can remove temporal punishment due for sins so dying for your faith could fall under that. And perfect contrition ( sorrow & detestation for your sins arising from a love for God) remits venial sins & mortals sins (CCC1452). Of course, only God know your heart and your reason for acting in a certain way, so only He would know to what extent your sins are forgiven and to what extent the temporal punishments due are removed.