None of this "marking " is in the catechism

How does this work with falling into mortal sin and going to confession ??

 Are marks being switched from a cross to 666 when we leave the confessional

If you do, then you don't fall into, rather you selfish and maliciously commit mortal sin.

Those who are seduced by Antichrist, "receive not the love of the truth",  are sent "the operation of error, to believe lying", and will be judged. Consequently, they will not even think about going to confession. Like e.g. in the Novus Ordo, confession has fallen into oblivion in most places, or is replaced by a chat session.

As to the words following, "And if any have not worshipped the beast nor his image, nor have received his inscription on their forehead, or on their hand," we must take them of both the living and the dead. And what this beast is, though it requires a more careful investigation, yet it is not inconsistent with the true faith to understand it of the ungodly city itself, and the community of unbelievers set in opposition to the faithful people and the city of God.

"His image" seems to me to mean his simulation, to wit, in those men who profess to believe, but live as unbelievers. For they pretend to be what they are not, and are called Christians, not from a true likeness but from a deceitful image. For to this beast belong not only the avowed enemies of the name of Christ and His most glorious city, but also the tares which are to be gathered out of His kingdom, the Church, in the end of the world.

And who are they who do not worship the beast and his image, if not those who do what the apostle says, "Be not yoked with unbelievers?" 2 Corinthians 6:14 For such do not worship, i.e., do not consent, are not subjected; neither do they receive the inscription, the brand of crime, on their forehead by their profession, on their hand by their practice.

Following St. Augustine, the mark of the beast is not a Pfizer vaccine, injected into the forehead, or AstraZeneca in the hand. Not only those who live during the last tribulation and witness the reign of Antichrist can receive the mark, called inscription by St. Augustine.

Those out of the Church, who don't believe, and those in the Church, who profess to believe but really don't, or do but live as unbelievers, will receive the mark of the beast. To receive the mark of the beast on the forehead means to profess the beast. To receive the mark of the beast on the hand means to follow the practice of the beast (even without profession).

Mortal can be forgiven unless you are dead.

So mortal sins Cant be forgiven during this period?

Sins are forgiven, given that the well known conditions are met, even during the reign of Antichrist. There is no teaching of the Church to the contrary.

But then who gets the mark

Following St. Augustine, all people ever, who end in hell.