The stone here is actually the Law. It’s the 10 commandments.
The bread here is the Spirit.
Or which one of you, if his son asks him for bread, will give him a stone?
If you read on Jesus says:
Or if he asks for a fish, will give him a serpent? If you then, who are evil, know how to give good gifts to your children, how much more will your Father who is in heaven give good things to those who ask him!
You can clearly see here the stone is related to the serpent. It is clear here that the Law is the weapon and condemnation is his food.
You would also note here that the good gift is not mention.
Luke tells us what this good gift is.
If you then, who are evil, know how to give good gifts to your children, how much more will the heavenly Father give the Holy Spirit to those who ask him!”
It’s the Spirit.
The fight was between whether to give into the Old Covenant or to embrace the New Covenant way of the Spirit.
Satan then took him to the top of the Temple. Again if you are familiar with the writings of Paul you will realise the Temple was Mount Sinai. The he asked him to jump from the Peak of the Temple. The Temple is Mount Sinai in Jerusalem.
He then offered him the position of the anti-Christ and the kingdoms of that world. A world under the dominance of the Old Covenant.